prof. RNDr. Čestmír Burdík, DrSc.

Čestmír Burdík - fotografie
e-mail: zobrazit e-mail
telefon: +420 22435 8549
místnost: 108b
www: http://kmlinux.fjfi.cvut.cz/~burdik
 
rozvrh
předmět kód vyučující zs ls zs kr. ls kr.
Kvantové grupy 101KVGR1 Burdík 2+0 z - - 2 -
Předmět:Kvantové grupy 101KVGR1prof.RNDr. Burdík Čestmír DrSc.2+0 Z-2-
Anotace:Kvantové algebry vznikly v 80-letech v pracích prof. L. D. Faddeeva a jeho Leningradské školy zabývající se integrabilními modely. Mají řadu aplikací v matematice a matematické fyzice jako např. při klasifikaci uzlů , v teorii integrabilních systémů a teorii strun.
Osnova:1. Motivace, koalgebra, bialgebra a Hopfova algebra.
2. Q-kalkul.
3. Kvantová algebra U_q (sl (2) a její reprezentace .
4. Kvantové grupa SL_q (2) a její reprezentace.
5. Q-oscilátorové algebry a jejich reprezentace.
6. Drinfeld-Jimbovy algebry.
7. Konečný-dimenzionální reprezentace Drinfeld-Jimbových algeber.
8. Quasitriangularita a univerzální R-matice.
Osnova cvičení:
Cíle:Znalosti:
Získat matematický základ teorie kvantových grup.

Schopnosti:
Umět používat teorii kvantových grup pro studium integrabilních systémů.
Požadavky:Základní kurzy matematické analýzy a lineární algebry
(dle přednášek na FJFI ČVUT v Praze 01MA1, 01MAA2-4, 01LAP, 01LAA2, TRLA).
Rozsah práce:
Kličová slova:Hopf algebra, q-calculus, Drinfeld double, quasitriangularita, universální R-matice.
Literatura:Povinná literatura:
[1] Anatoli Klimyk, Konrad Schmudgen , Quantum groups and their representations.Springer-Verlag-Berlin 1997

Doporučená literatura:
[2] Podles, P.; Muller,E., Introduction to quantum groups, arXiv:q-alg/9704002.
[3] Kassel, Christian (1995), Quantum groups, Graduate Texts in Mathematics,155, Berlin, New York: Springer-Verlag, MR1321145, ISBN 978-0-387-94370-1

Lineární programování01LIP Burdík 2+1 z,zk - - 3 -
Předmět:Lineární programování01LIPprof.RNDr. Burdík Čestmír DrSc.-2+1 Z,ZK-3
Anotace:Předmět se zabývá speciálními úlohami na vázané extrémy funkcí více proměnných(funkce je lineární a vazbové podmínky mají tvar lineárních rovnic a nerovnic).
Osnova:Tvary úloh LP, dualita. Lineární rovnice a nerovnice, konvexní mnohostěn, bazické přípustné řešení, komplementarita. Metody: simplexová, duální simplexová, primárně-duální, revidovaná. Princip dekompozice, dopravní problém. Diskrétní LP (Gomoryho algoritmus). Aplikace LP v teorii her - maticové hry. Časově polynomiální algoritmy LP (Chačijan, Karmarkar).
Osnova cvičení:1. Test optimality přípustného řešení, poznat krajní bod množiny přípustných řešení, sestavení duální úlohy.
2. Simplexová metoda, duální simplexová metoda, primárně duální simplexová metoda.
3. Gomoryho algoritmus, celočíselný algoritmus.
4. Aplikace v teorii her.
Cíle:Znalosti:
Matematický základ o soustavách lineárních rovnic a nerovnic.

Schopnosti:
Umět používat probrané algoritmy na řešení konkrétních úloh z praxe.
Požadavky:Základní kurzy matematické analýzy a lineární algebry
(dle přednášek na FJFI ČVUT v Praze 01MA1, 01MAA2-4, 01LAA1, 01LAA2).

Rozsah práce:
Kličová slova:Přípustné a optimální řešení, bazické řešení, krajní bod, simplexová metoda, slabá komplementarita, celočíselné programování.
Literatura:Povinná literatura:
[1] Ján Plesník, Jitka Dupačová, Milan Vlach: Lineárne programovanie, ALFA, Bratislava 1990, 1. Vydání,
[2] Libuše Grygarová: Úvod do lineárního programování, skripta, Státní pedagogické nakladatelství, Praha 1975, 1. vydání, skripta

Doporučená literatura:
[3] Jitka Dupačová:Lineární programování, SPN, Praha 1982,
[4] Prof.Ing.Josef Jablonský,CSc.: Operační výzkum, Kvantitativní modely pro ekonomické rozhodování, Professional Publishing, 2002

Lineární programování B01LIPB Burdík 2+2 z,zk - - 4 -
Předmět:Lineární programování B01LIPBprof.RNDr. Burdík Čestmír DrSc.2+2 Z,ZK-4-
Anotace:Cílem přednášky je matematická formulace simplexového algoritmu úlohy lineárního programovaní. V matematickém jazyce se formulují a dokazují věty pro primární a duální úlohu. V aplikacích se studuje použití v teorii her, pro dopravní problémy a úlohy celočíselného programování.
Osnova:1. Úloha lineárního programování.
2. Kritérium optimality.
3. Simplexový algoritmus.
4. Dvoufázová simplexová metoda.
5. Ukázka vypočtu a zacyklení.
6. Primární a duální úloha.
7. Věta o dualitě.
8. Farkašova věta.
9. Aplikace v teorii her.
10. Dopravní problém.
11. Celočíselné programování.
12. Gomoryho algoritmus.
13. Parametrické programování.
Osnova cvičení:1. Úloha lineárního programování, podmínka optimality a neomezenost.
2. Simplexová metoda.
3. Dvojfázová simplexová metoda.
4. Duální simplexová metoda.
5. Příklad z teorie her.
6. Gomoryho algoritmus.
7. Kvadratické programování.
Cíle:Znalosti:
Matematický základ o soustavách lineárních rovnic a nerovnic a optimalizace.

Schopnosti:
Umět používat probrané algoritmy na řešení konkrétních úloh z praxe.
Požadavky:Základní kurzy matematické analýzy a lineární algebry
(dle přednášek na FJFI ČVUT v Praze 01MAB1, 01MAB2-4, 01LAB1, 01LAB2).
Rozsah práce:
Kličová slova:Přípustné a optimální řešení, bazické řešení, krajní bod, simplexová metoda, slabá komplementarita, celočíselné programování.
Literatura:Povinná literatura:
[1] Ján Plesník, Jitka Dupačová, Milan Vlach: Lineárne programovanie, ALFA, Bratislava 1990, 1. Vydání,
[2] Libuše Grygarová: Úvod do lineárního programování, skripta, Státní pedagogické nakladatelství, Praha 1975, 1. vydání, skripta

Doporučená literatura:
[3] Jitka Dupačová: Lineární programování, Státní pedagogické nakladatelství, Praha 1982, 1. vydání, skripta,
[4] Prof. Ing. Josef Jablonský, CSc.: Operační výzkum, Kvantitativní modely pro ekonomické rozhodování, Professional Publishing, 2002

Nelineární programování01NELI Burdík 3+0 zk - - 4 -
Předmět:Nelineární programování01NELIprof.RNDr. Burdík Čestmír DrSc.3+0 ZK-4-
Anotace:Konvexní optimalizace nachází své uplatnění
v mnoha oblastech aplikované matematiky. V přednášce jsou formulovány základy teorie
konvexní analýzy a rozvíjeny algoritmy pro
nepodmíněnou optimalizaci a optimalizaci s vazbami typu rovností. Je studována teorie
duality a v návaznosti metoda vnitřního bodu.
Osnova:1. Afinní a konvexní množiny, operace zachovávající konvexitu, dělící a podpůrná nadrovina.
2. Konvexní funkce, základní vlastnosti a příklady, operace, které zachovávají konvexnost funkcí, sdružené funkce, quasikonvexní funkce, log-konkávní a log-konvexní funkce.
3. Optimalizační problém ve standartním tvaru, konvexní optimalizační problém, quasikonvexní optimalizace, lineární optimalizace, kvadratické optimalizace, geometrické programování.
4. Dualita, Lagrangeův duální problém, slabá a silná dualita.
5. Numerická lineární algebra , maticová struktura a složitost algoritmu, řešení lineárních rovnic s maticemi, LU a Choleského faktorizace, bloková eliminace a inverzní lemma.
6. Neomezené minimalizace, gradientní metoda, metoda největšího spádu, Newtonova metoda, self-concondartní funkce.
7. Minimalizace pro úlohy s rovnostmi, odstraňování rovností , Newtonova metoda začínající v nepřípustném bodě.
8. Metoda vnitřního bodu, logaritmická bariérové funkce , bariérové metody.
9. Lineární komplementarity problém a kvadratické programování.
Osnova cvičení:
Cíle:Znalosti:
Matematický základ konvexní optimalizace.

Schopnosti:
Umět používat algoritmy nelineární optimalizace v praxi.
Požadavky:Základní kurzy matematické analýzy a lineární algebry
(dle přednášek na FJFI ČVUT v Praze 01MA1, 01MAA2-4, 01LAP, 01LAA2, 01LINPA).
Rozsah práce:
Kličová slova:Nelineární optimalizace, konvexní množiny, konvexní funkce, Lagrangeova dualita, Kuhn-Tuckerovy podmínky, neomezená optimalizace, optimalizace
s vazbami.
Literatura:Povinná literatura:
[1] Stephen Boyd and Lieven Vandenberghe, Convex optimization, Cambridge University Press 2004

Doporučená literatura:
[2] L. Lukšan, Matematické programování, Institute of Computer Science, Academy of Sciences of the Czech Republic, Report 1034

Topologie01TOP Burdík 2+0 zk - - 2 -
Předmět:Topologie01TOPprof.RNDr. Burdík Čestmír DrSc.2+0 ZK-2-
Anotace:Cílem přednášky je systematizovat a prohloubit základní pojmy obecné topologie.
Osnova:1. Struktura na množině.
2. Reálná čísla a rovina.
3. Soubory, součiny a sumy.
4. Grafy.
5. Matematické struktury.
6. Abstraktní prostory.
7. Struktura topologických prostorů.
8. Oddělování.
9. Hausdorffovy prostory.
10. Normální prostory.
11. Kompaktní prostory.
12. Topologie metriky.
13. Metrické prostory.
Osnova cvičení:
Cíle:Znalosti:
Matematický základ obecné topologie.

Schopnosti:
Umět myslet v rámci schématu, definice, věta a důkaz a tento používat v obecné topologii.
Požadavky:Základní kurzy matematické analýzy a lineární algebry (dle přednášek na FJFI ČVUT v Praze 01MA1, 01MAA2-4, 01LAP, 01LAA2).
Rozsah práce:
Kličová slova:Topologický prostor, topologie součinu, topologie podprostoru, souvislé prostory, kompaktní prostory.
Literatura:Povinná literatura:
[1] Adámek, Koubek, Reiterman: Základy obecné topologie, SNTL Praha, 1977.

Doporučená literatura:
[2] D. Krupka, O. Krupková: Topologie a geometrie, Obecná topologie, SPN Praha, 1989.

Základy teorie reprezentací a Lieových algeber01TRLA Burdík - - 2+0 zk - 2
Předmět:Základy teorie reprezentací a Lieových algeber01TRLAprof.RNDr. Burdík Čestmír DrSc.-2+0 ZK-2
Anotace:Lieovy algebry jsou neodmyslitelnou součástí teorií v mnoha oblastech přírodních věd. V přednášce jsou formulovány elementární základy teorie Lievých algeber a jejich reprezentací.
Osnova:1. Definice a příklady Lieových algeber.
2. Vztah mezi Lieovou grupou a Lieovou algebrou.
3. Definice reprezentace Lieovy algebry a Lieovy grupy, adjungované reprezentace.
4. Obalová algebra Lieovy algebry. Kazimirovy elementy.
5. Strukturní teorie, podalgebry a ideály Lieovy algebry.
6. Přímý a polopřímý součet Lieových algeber.
7. Nilpotentní, řešitelné,poloprosté a prosté Lieovy algebry.
8. Cartanův rozklad, konstrukce prosté Lieovy algebry pomocí Cartanovy matice.
9. Kac-Moodyho algebry.
10. Superalgebry.
11. Příklady použití v matematice a matematické fyzice.
Osnova cvičení:
Cíle:Znalosti:
Získat matematický základ pro teorii reprezentací Lieových algeber.

Schopnosti:
Umět používat reprezentace v aplikacích.
Požadavky:Základní kurzy matematické analýzy a lineární algebry (dle přednášek na FJFI ČVUT v Praze 01MA1, 01MAA2-4, 01LAP, 01LAA2).

Rozsah práce:
Kličová slova:Lieova algebra, Lieova grupa, obalová algebra, Cartanova matice, reprezentace, Kac-Moody algebry, superalgebry.
Literatura:Povinná literatura:
[1] Hall, Brian C.: Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Springer, ISBN 0-387-40122-9, 2003.

Doporučená literatura:
[2] Marian Fecko: Diferencialná geometria a lieovy grupy pre fyzikov, IRIS, Bratislava, 2004.

Knihy

2008

Burdík, Č. and Navrátil, O., Rovnice matematicke fyziky, Česká technika - nakladatelství ČVUT, 2008,
BiBTeX
@BOOK{Burdik08:149,
  title = {{Rovnice matematicke fyziky}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Praha},
  edition = {1},
  publisher = {{\v C}esk{\' a} technika - nakladatelstv{\'\i} {\v C}VUT},
  year = {2008},
  pages = {113}
}

Články v časopisech

2013

Burdík, Č. and Navrátil, O., Extremal Vectors for Verma-Type Representations of su(2,2), Physics of Atomic Nuclei 76 (2013) , 977-982
BiBTeX
@ARTICLE{Burdik13:213,
  title = {{Extremal Vectors for Verma-Type Representations of su(2,2)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Physics of Atomic Nuclei},
  year = {2013},
  volume = {76},
  number = {8},
  pages = {977--982}
}
Burdík, Č. and Navrátil, O., Extremal Vectors for Verma-Type Representation of B2, Acta Polytechnica 53 (2013) , 399-404
BiBTeX
@ARTICLE{Burdik13:213,
  title = {{Extremal Vectors for Verma-Type Representation of B2}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Acta Polytechnica},
  year = {2013},
  volume = {53},
  number = {5},
  pages = {399--404}
}

2012

Burdík, Č. and Sutulin, A. and Krivonos, S., Generalized Nonlinear Chiral Supermultiplet, Journal of Physics: Conference Series 2012 (2012) , 1-10
BiBTeX
@ARTICLE{Burdik12:196,
  title = {{Generalized Nonlinear Chiral Supermultiplet}},
  author = {Burd{\'\i}k, {\v C}. and Sutulin, A. and Krivonos, S.},
  journal = {Journal of Physics: Conference Series},
  year = {2012},
  volume = {2012},
  number = {343},
  pages = {1--10}
}
Burdík, Č. and Reshetnyak, A., On representations of Higher Spin symmetry algebras for mixed-symmetry HS fields on AdS-spaces. Lagrangian formulation, Journal of Physics: Conference Series 2012 (2012) , 1-25
BiBTeX
@ARTICLE{Burdik12:196,
  title = {{On representations of Higher Spin symmetry algebras for mixed-symmetry HS fields on AdS-spaces. Lagrangian formulation}},
  author = {Burd{\'\i}k, {\v C}. and Reshetnyak, A.},
  journal = {Journal of Physics: Conference Series},
  year = {2012},
  volume = {2012},
  number = {343},
  pages = {1--25}
}
Burdík, Č. and Ananikyan, N. and Lazaryan, H., Magnetization and concurrence on decorated zigzag ladder, Journal of Physics: Conference Series 2012 (2012) , 1-10
BiBTeX
@ARTICLE{Burdik12:196,
  title = {{Magnetization and concurrence on decorated zigzag ladder}},
  author = {Burd{\'\i}k, {\v C}. and Ananikyan, N. and Lazaryan, H.},
  journal = {Journal of Physics: Conference Series},
  year = {2012},
  volume = {2012},
  number = {343},
  pages = {1--10}
}
Burdík, Č. and Navrátil, O. and Pošta, S., Extremal Vectors for Verma Type Factor Representations of Uq(sl(3,C)), Physics of Particles and Nuclei 43 (2012) , 700-702
BiBTeX
@ARTICLE{Burdik12:194,
  title = {{Extremal Vectors for Verma Type Factor Representations of Uq(sl(3,C))}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  journal = {Physics of Particles and Nuclei},
  year = {2012},
  volume = {43},
  number = {5},
  pages = {700--702}
}
Burdík, Č. and Ananikyan, N. and Ananikyan, L. and Chakhmakhchyan, L., Thermal entanglement of the spin-1/2 diamond chain, Journal of Physics: Conference Series 2012 (2012) , 1-15
BiBTeX
@ARTICLE{Burdik12:196,
  title = {{Thermal entanglement of the spin-1/2 diamond chain}},
  author = {Burd{\'\i}k, {\v C}. and Ananikyan, N. and Ananikyan, L. and Chakhmakhchyan, L.},
  journal = {Journal of Physics: Conference Series},
  year = {2012},
  volume = {2012},
  number = {343},
  pages = {1--15}
}

2011

Burdík, Č. and Navrátil, O., The New Formulas for the Eigenvectors of the Gaudin Model in the so(5) Case, Physics of Atomic Nuclei 74 (2011) , 852-862
BiBTeX
@ARTICLE{Burdik11:187,
  title = {{The New Formulas for the Eigenvectors of the Gaudin Model in the so(5) Case}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Physics of Atomic Nuclei},
  year = {2011},
  volume = {74},
  number = {6},
  pages = {852--862},
  month = {6}
}
Burdík, Č. and Navrátil, O., Heighest Weight Representation for Sklyanin Alegebra sl(3)(u) with Application to the Gaudin Model, Physics of Atomic Nuclei 74 (2011) , 863-869
BiBTeX
@ARTICLE{Burdik11:187,
  title = {{Heighest Weight Representation for Sklyanin Alegebra sl(3)(u) with Application to the Gaudin Model}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Physics of Atomic Nuclei},
  year = {2011},
  volume = {74},
  number = {6},
  pages = {863--869},
  month = {6}
}

2010

Burdík, Č. and Havlíček, M. and Tolstoy, V.N. and Asherova, RM, q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U-q(u(n, 1)), Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 6 (2010) , 1-13
BiBTeX
@ARTICLE{Burdik10:167,
  title = {{q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U-q(u(n, 1))}},
  author = {Burd{\'\i}k, {\v C}. and Havl{\'\i}{\v c}ek, M. and Tolstoy, V.N. and Asherova, RM},
  journal = {Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)},
  year = {2010},
  volume = {6},
  number = {10},
  pages = {1--13}
}

2009

Burdík, Č. and Nersessian, A., Remarks on Multi-Dimensional Conformal Mechanics, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5 (2009) , 1-10
BiBTeX
@ARTICLE{Burdik09:156,
  title = {{Remarks on Multi-Dimensional Conformal Mechanics}},
  author = {Burd{\'\i}k, {\v C}. and Nersessian, A.},
  journal = {Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)},
  year = {2009},
  volume = {5},
  number = {4},
  pages = {1--10}
}
Burdík, Č. and Navrátil, O. and Pošta, S., The adjoint representation of quantum algebra Uq(sl2), Journal of Nonlinear Mathematical Physics 16 (2009) , 63-75
BiBTeX
@ARTICLE{Burdik09:159,
  title = {{The adjoint representation of quantum algebra Uq(sl2)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  journal = {Journal of Nonlinear Mathematical Physics},
  year = {2009},
  volume = {16},
  number = {1},
  pages = {63--75},
  month = {3}
}

2008

Burdík, Č. and Navrátil, O., New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case, Regular and Chaotic Dynamics 13 (2008) , 403-416
BiBTeX
@ARTICLE{Burdik08:149,
  title = {{New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Regular and Chaotic Dynamics},
  year = {2008},
  volume = {13},
  number = {5},
  pages = {403--416},
  month = {october}
}
Burdík, Č. and Havlíček, M. and Navrátil, O. and Pošta, S., Ideals of the enveloping algebra U(osp(1,2)), Journal of Generalized Lie Theory and Applications 2 (2008) , 132-136
BiBTeX
@ARTICLE{Burdik08:149,
  title = {{Ideals of the enveloping algebra U(osp(1,2))}},
  author = {Burd{\'\i}k, {\v C}. and Havl{\'\i}{\v c}ek, M. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  journal = {Journal of Generalized Lie Theory and Applications},
  year = {2008},
  volume = {2},
  number = {3},
  pages = {132--136},
  month = {october}
}

2007

Burdík, Č. and Navrátil, O. and Pošta, S., Two-Dimensional Matrix Calogero Model of the BC2 Type, Physics of Atomic Nuclei 70 (2007) , 491-495
BiBTeX
@ARTICLE{Burdik07:125,
  title = {{Two-Dimensional Matrix Calogero Model of the BC2 Type}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  journal = {Physics of Atomic Nuclei},
  year = {2007},
  volume = {70},
  number = {3},
  pages = {491--495},
  month = {march}
}
Burdík, Č. and Navrátil, O. and Pošta, S., Structure of the Enveloping Algebras, Acta Polytechnica 47 (2007) , 25-31
BiBTeX
@ARTICLE{Burdik07:140,
  title = {{Structure of the Enveloping Algebras}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  journal = {Acta Polytechnica},
  year = {2007},
  volume = {47},
  number = {2},
  pages = {25--31},
  month = {btrezen}
}
Burdík, Č. and Navrátil, O., Dirac Formulation of Free Open String, The Old and New Concepts of Physics 4 (2007) , 487-503
BiBTeX
@ARTICLE{Burdik07:138,
  title = {{Dirac Formulation of Free Open String}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {The Old and New Concepts of Physics},
  year = {2007},
  volume = {4},
  number = {4},
  pages = {487--503},
  month = {december}
}

2006

Burdík, Č. and Paal, E. and Virkepu, J., SO(2) and Hamilton-Dirac mechanics, Journal of Nonlinear Mathematical Physics 4 (2006) , 37-43
BiBTeX
@ARTICLE{Burdik06:125,
  title = {{SO(2) and Hamilton-Dirac mechanics}},
  author = {Burd{\'\i}k, {\v C}. and Paal, E. and Virkepu, J.},
  journal = {Journal of Nonlinear Mathematical Physics},
  year = {2006},
  volume = {4},
  number = {13},
  pages = {37--43},
  month = {january}
}
Burdík, Č. and Navrátil, O. and Pošta, S., On the Matrix 3x3 Exactly Solvable Models of the Type G2, Journal of Nonlinear Mathematical Physics 4 (2006) , 27-36
BiBTeX
@ARTICLE{Burdik06:125,
  title = {{On the Matrix 3x3 Exactly Solvable Models of the Type G2}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  journal = {Journal of Nonlinear Mathematical Physics},
  year = {2006},
  volume = {4},
  number = {13},
  pages = {27--36}
}
Burdík, Č. and Krivonos, S. and Shcherbakov, A., Hyper-Kahler Geometry via Dualization, Czechoslovak Journal of Physics 56 (2006) , 1099-1103
BiBTeX
@ARTICLE{Burdik06:125,
  title = {{Hyper-Kahler Geometry via Dualization}},
  author = {Burd{\'\i}k, {\v C}. and Krivonos, S. and Shcherbakov, A.},
  journal = {Czechoslovak Journal of Physics},
  year = {2006},
  volume = {56},
  number = {10},
  pages = {1099--1103},
  month = {october}
}
Burdík, Č. and Haysak, M. and Chalupka, S., Hyperspherical Approach to Description of Electron Correlation in Negative Ion of Exciton, Czechoslovak Journal of Physics 56 (2006) , 1461-1466
BiBTeX
@ARTICLE{Burdik06:125,
  title = {{Hyperspherical Approach to Description of Electron Correlation in Negative Ion of Exciton}},
  author = {Burd{\'\i}k, {\v C}. and Haysak, M. and Chalupka, S.},
  journal = {Czechoslovak Journal of Physics},
  year = {2006},
  volume = {56},
  number = {12},
  pages = {1461--1466},
  month = {december}
}
Burdík, Č. and Pošta, S. and Navrátil, O., On Three Particle Matrix Calogero Models, Physics Letters A 352 (2006) , 362-370
BiBTeX
@ARTICLE{Burdik06:125,
  title = {{On Three Particle Matrix Calogero Models}},
  author = {Burd{\'\i}k, {\v C}. and Po{\v s}ta, S. and Navr{\' a}til, O.},
  journal = {Physics Letters A},
  year = {2006},
  volume = {352},
  number = {352},
  pages = {362--370},
  month = {january}
}

2005

Burdík, Č. and Navrátil, O. and Pošta, S., On Matrix Solvable Calogero Models of B2 Type, Journal of Geometry and Symmetry in Physics 6 (2005) , 11-15
BiBTeX
@ARTICLE{Burdik05:125,
  title = {{On Matrix Solvable Calogero Models of B2 Type}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  journal = {Journal of Geometry and Symmetry in Physics},
  year = {2005},
  volume = {6},
  number = {6},
  pages = {11--15}
}
Burdík, Č. and Navrátil, O., The q-Boson-Fermion Realizations of the Quantum Superalgebra Uq(osp(1/2)), Physics of Atomic Nuclei 68 (2005) , 1643-1645
BiBTeX
@ARTICLE{Burdik05:116,
  title = {{The q-Boson-Fermion Realizations of the Quantum Superalgebra Uq(osp(1/2))}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Physics of Atomic Nuclei},
  year = {2005},
  volume = {68},
  number = {10},
  pages = {1643--1645},
  month = {October}
}
Burdík, Č. and Navrátil, O., Normal Ordering for the Deformed Heisenberg Algebra Involving the Reflection Operators, Journal of Physics A: Mathematical and General 38 (2005) , 2305-2310
BiBTeX
@ARTICLE{Burdik05:115,
  title = {{Normal Ordering for the Deformed Heisenberg Algebra Involving the Reflection Operators}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Journal of Physics A: Mathematical and General},
  year = {2005},
  volume = {38},
  number = {2},
  pages = {2305--2310},
  month = {February}
}
Burdík, Č. and Navrátil, O., A Method for Construction of the Matrix Solvable Models, Journal of Physics A: Mathematical and General 38 (2005) , 1533-1542
BiBTeX
@ARTICLE{Burdik05:115,
  title = {{A Method for Construction of the Matrix Solvable Models}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Journal of Physics A: Mathematical and General},
  year = {2005},
  volume = {38},
  number = {2},
  pages = {1533--1542},
  month = {February}
}
Burdík, Č. and Krivonos, S. and Scherbakov, A., N=4 Supersymmetric Eguchi-Hanson Sigma Model in d=1, Czechoslovak Journal of Physics 55 (2005) , 1357-1364
BiBTeX
@ARTICLE{Burdik05:117,
  title = {{N=4 Supersymmetric Eguchi-Hanson Sigma Model in d=1}},
  author = {Burd{\'\i}k, {\v C}. and Krivonos, S. and Scherbakov, A.},
  journal = {Czechoslovak Journal of Physics},
  year = {2005},
  volume = {55},
  number = {11},
  pages = {1357--1364},
  month = {november}
}

2004

Burdík, Č. and Haysak, M. and Nagy, M., The negative and positive charged two-dimensional three-body systems in addiabatic hyperspherical approach, Czechoslovak Journal of Physics 54 (2004) , 1191-1197
BiBTeX
@ARTICLE{Burdik04:105,
  title = {{The negative and positive charged two-dimensional three-body systems in addiabatic hyperspherical approach}},
  author = {Burd{\'\i}k, {\v C}. and Haysak, M. and Nagy, M.},
  journal = {Czechoslovak Journal of Physics},
  year = {2004},
  volume = {54},
  number = {11},
  pages = {1191--1197},
  month = {listopad}
}
Andrle, M. and Burdík, Č. and Gazeau, J.P., Bernau Spline Wavelets and Sturmian Sequences, The Journal of Fourier Analysis and Application 10 (2004) , 269-300
BiBTeX
@ARTICLE{Andrle04:105,
  title = {{Bernau Spline Wavelets and Sturmian Sequences}},
  author = {Andrle, M. and Burd{\'\i}k, {\v C}. and Gazeau, J.P.},
  journal = {The Journal of Fourier Analysis and Application},
  year = {2004},
  volume = {10},
  number = {3},
  pages = {269--300},
  month = {November}
}

2002

Burdík, Č. and Navrátil, O., Nonlinear superposition formulae based on the Lie group SO(n+1,n), Journal of Physics A: Mathematical and General 35 (2002) , 2431-2440
BiBTeX
@ARTICLE{Burdik02:806,
  title = {{Nonlinear superposition formulae based on the Lie group SO(n+1,n)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Journal of Physics A: Mathematical and General},
  year = {2002},
  volume = {35},
  number = {2},
  pages = {2431--2440},
  month = {February}
}

2001

Burdík, Č. and Pashnev, A. and Tsulaia, M., The Lagrangian description of representations of the Poincare group, Nuclear Physics B - Proceedings Supplements 102 (2001) , 285-292
BiBTeX
@ARTICLE{Burdik01:145,
  title = {{The Lagrangian description of representations of the Poincare group}},
  author = {Burd{\'\i}k, {\v C}. and Pashnev, A. and Tsulaia, M.},
  journal = {Nuclear Physics B - Proceedings Supplements},
  year = {2001},
  volume = {102},
  number = {2},
  pages = {285--292},
  month = {april}
}
Burdík, Č. and Pashnev, A. and Tsulaia, M., On the Mixed Symmetry Irreducible Representations of the Poincare Group in the BRST Approach, Modern Physics Letters A A16 (2001) , 731-746
BiBTeX
@ARTICLE{Burdik01:688,
  title = {{On the Mixed Symmetry Irreducible Representations of the Poincare Group in the BRST Approach}},
  author = {Burd{\'\i}k, {\v C}. and Pashnev, A. and Tsulaia, M.},
  journal = {Modern Physics Letters A},
  year = {2001},
  volume = {A16},
  number = {3},
  pages = {731--746}
}

2000

Burdík, Č. and Pashnev, A. and Tsulaia, M., Auxiliary Representations of Lie Algebras and the BRST Constructions, Modern Physics Letters A 15 (2000) , 281-291
BiBTeX
@ARTICLE{Burdik00:363,
  title = {{Auxiliary Representations of Lie Algebras and the BRST Constructions}},
  author = {Burd{\'\i}k, {\v C}. and Pashnev, A. and Tsulaia, M.},
  journal = {Modern Physics Letters A},
  year = {2000},
  volume = {15},
  number = {4},
  pages = {281--291}
}
Burdík, Č. and Grozman, P. and Leites, D. and Sergeev, A., Realizations of Lie Algebras and Superalgebras Via Creation and Annihilations, Theoretical and Mathematical Physics 124 (2000) , 1048-1058
BiBTeX
@ARTICLE{Burdik00:363,
  title = {{Realizations of Lie Algebras and Superalgebras Via Creation and Annihilations}},
  author = {Burd{\'\i}k, {\v C}. and Grozman, P. and Leites, D. and Sergeev, A.},
  journal = {Theoretical and Mathematical Physics},
  year = {2000},
  volume = {124},
  number = {2},
  pages = {1048--1058}
}
Andrle, M. and Burdík, Č. and Gazeau, J. and Krejcar, R., Wavelets Multiresolutions for the Fibonacci Chain, Journal of Physics A: Mathematical and General 33 (2000) , L47-L51
BiBTeX
@ARTICLE{Andrle00:363,
  title = {{Wavelets Multiresolutions for the Fibonacci Chain}},
  author = {Andrle, M. and Burd{\'\i}k, {\v C}. and Gazeau, J. and Krejcar, R.},
  journal = {Journal of Physics A: Mathematical and General},
  year = {2000},
  volume = {33},
  number = {4},
  pages = {L47--L51},
  month = {January}
}

1999

Burdík, Č. and Navrátil, O., The q-Boson Realizations of the Quantum Groups Uq(Dn), Journal of Physics A: Mathematical and General 32 (1999) , 6141-6147
BiBTeX
@ARTICLE{Burdik99:206,
  title = {{The q-Boson Realizations of the Quantum Groups Uq(Dn)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Journal of Physics A: Mathematical and General},
  year = {1999},
  volume = {32},
  number = {34},
  pages = {6141--6147},
  month = {August}
}
Burdík, Č. and Navrátil, O., The q-boson Realizations of the Quantum Groups U_q(D_n), Journal of Physics A: Mathematical and General 32 (1999) , 6141-6147
BiBTeX
@ARTICLE{Burdik99:203,
  title = {{The q-boson Realizations of the Quantum Groups U_q(D_n)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Journal of Physics A: Mathematical and General},
  year = {1999},
  volume = {32},
  number = {34},
  pages = {6141--6147},
  month = {September}
}
Burdík, Č. and Navrátil, O., The q_Boson Realizations of the Quantum Group U_q(C_n), International Journal of Modern Physics A 14 (1999) , 4491-4500
BiBTeX
@ARTICLE{Burdik99:229,
  title = {{The q_Boson Realizations of the Quantum Group U_q(C_n)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {International Journal of Modern Physics A},
  year = {1999},
  volume = {14},
  number = {28},
  pages = {4491--4500},
  month = {November}
}
Burdík, Č. and Navrátil, O., The q-Bosom Realizations of the Quantum Group Uq(Cn), International Journal of Modern Physics A 14 (1999) , 4491-4500
BiBTeX
@ARTICLE{Burdik99:212,
  title = {{The q-Bosom Realizations of the Quantum Group Uq(Cn)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {International Journal of Modern Physics A},
  year = {1999},
  volume = {14},
  number = {28},
  pages = {4491--4500},
  month = {November}
}

1998

Burdík, Č. and Navrátil, O., The q-Boson Realizations of the Quantum Groups Uq(Bn), Czechoslovak Journal of Physics 48 (1998) , 1301-1306
BiBTeX
@ARTICLE{Burdik98:603,
  title = {{The q-Boson Realizations of the Quantum Groups Uq(Bn)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Czechoslovak Journal of Physics},
  year = {1998},
  volume = {48},
  number = {11},
  pages = {1301--1306}
}
Burdík, Č. and Krejcar, R. and Gazeau, J. and Frougny, C., Beta-integers as natural Counting Systems for quasicrystals, Journal of Physics A: Mathematical and General 31 (1998) , 6449-6472
BiBTeX
@ARTICLE{Burdik98:254,
  title = {{Beta-integers as natural Counting Systems for quasicrystals}},
  author = {Burd{\'\i}k, {\v C}. and Krejcar, R. and Gazeau, J. and Frougny, C.},
  journal = {Journal of Physics A: Mathematical and General},
  year = {1998},
  volume = {31},
  number = {30},
  pages = {6449--6472},
  month = {July}
}

1996

Burdík, Č. and Navrátil, O., Vertex Operators for the Central Extension of the Quantum Affine Algebra Uq(sl2), Czechoslovak Journal of Physics 46 (1996) , 1203-1210
BiBTeX
@ARTICLE{Burdik96:506,
  title = {{Vertex Operators for the Central Extension of the Quantum Affine Algebra Uq(sl2)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Czechoslovak Journal of Physics},
  year = {1996},
  volume = {46},
  number = {12},
  pages = {1203--1210}
}
Burdík, Č. and Navrátil, O., Boson realization of Yangians Y(sl(2)) and Y(sl(3)), Czechoslovak Journal of Physics 46 (1996) , 145-150
BiBTeX
@ARTICLE{Burdik96:482,
  title = {{Boson realization of Yangians Y(sl(2)) and Y(sl(3))}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Czechoslovak Journal of Physics},
  year = {1996},
  volume = {46},
  number = {2},
  pages = {145--150},
  month = {FEB}
}

1994

Burdík, Č. and Navrátil, O., The q-boson Realizations of the Quantum Groups B2 and C2, Czechoslovak Journal of Physics 44 (1994) , -
BiBTeX
@ARTICLE{Burdik94:429,
  title = {{The q-boson Realizations of the Quantum Groups B2 and C2}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  journal = {Czechoslovak Journal of Physics},
  year = {1994},
  volume = {44},
  pages = {--}
}

1993

Burdík, Č. and Navrátil, O. and Thoma, M., A New Class of Realizations of Lie Algebra G2, Czechoslovak Journal of Physics 43 (1993) , 697-703
BiBTeX
@ARTICLE{Burdik93:429,
  title = {{A New Class of Realizations of Lie Algebra G2}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Thoma, M.},
  journal = {Czechoslovak Journal of Physics},
  year = {1993},
  volume = {43},
  pages = {697--703}
}
Burdík, Č. and Černý, L. and Navrátil, O., The q-boson Realizations of the Quantum Group Uq(sl(n,C), Journal of Physics A: Mathematical and Theoretical 26 (1993) , L83-L88
BiBTeX
@ARTICLE{Burdik93:429,
  title = {{The q-boson Realizations of the Quantum Group Uq(sl(n,C)}},
  author = {Burd{\'\i}k, {\v C}. and {\v C}ern{\' y}, L. and Navr{\' a}til, O.},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  year = {1993},
  volume = {26},
  number = {3},
  pages = {L83--L88},
  month = {FEB}
}
Burdík, Č. and Hellinger, P., The Quantum Double for a Nonstandard Deformation of a Borel Subalgebra sl(2), Preprint Charles University Prague (1993) , -
BiBTeX
@ARTICLE{Burdik93:448,
  title = {{The Quantum Double for a Nonstandard Deformation of a Borel Subalgebra sl(2)}},
  author = {Burd{\'\i}k, {\v C}. and Hellinger, P.},
  journal = {Preprint Charles University Prague},
  year = {1993},
  pages = {--}
}

1986

Burdík, Č., A NEW CLASS OF REALIZATIONS OF THE LIE-ALGEBRA SP(N,R), Journal of Physics A: Mathematical and General 19 (1986) , 2456-2471
BiBTeX
@ARTICLE{Burdik86:177,
  title = {{A NEW CLASS OF REALIZATIONS OF THE LIE-ALGEBRA SP(N,R)}},
  author = {Burd{\'\i}k, {\v C}.},
  journal = {Journal of Physics A: Mathematical and General},
  year = {1986},
  volume = {19},
  number = {13},
  pages = {2456--2471},
  month = {SEP}
}

Články ve sbornících

2010

Burdík, Č. and Gevorkyan, A. and Oganasyan, K.B, Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations, QUANTUM THEORY: RECONSIDERATION OF FOUNDATIONS - 5, (2010) , 251-258, AIP Conference Proceedings
BiBTeX
@INPROCEEDINGS{Burdik10:176,
  title = {{Quantum Harmonic Oscillator Subjected to Quantum Vacuum Fluctuations}},
  author = {Burd{\'\i}k, {\v C}. and Gevorkyan, A. and Oganasyan, K.B},
  address = {New York},
  booktitle = {{QUANTUM THEORY: RECONSIDERATION OF FOUNDATIONS - 5}},
  publisher = {AIP Conference Proceedings},
  year = {2010},
  pages = {251--258}
}

2009

Burdík, Č. and Navrátil, O., Decomposition of the Enveloping Algebra so(5), Generalized Lie Theory in Mathematics,Physics and Beyond, (2009) , 297-302, Springer
BiBTeX
@INPROCEEDINGS{Burdik09:166,
  title = {{Decomposition of the Enveloping Algebra so(5)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Berlin},
  booktitle = {{Generalized Lie Theory in Mathematics,Physics and Beyond}},
  publisher = {Springer},
  year = {2009},
  pages = {297--302}
}

2008

Burdík, Č. and Navrátil, O. and Pošta, S., The Adjoint Representation of Quantum Algebra U_q(sl(2)), Supersymmetries and Quantum Symmetries, (2008) , 233-236, JINR
BiBTeX
@INPROCEEDINGS{Burdik08:149,
  title = {{The Adjoint Representation of Quantum Algebra U_q(sl(2))}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  address = {Dubna},
  booktitle = {{Supersymmetries and Quantum Symmetries}},
  publisher = {JINR},
  year = {2008},
  pages = {233--236}
}

2007

Burdík, Č. and Navrátil, O. and Pošta, S., Structure of the Enveloping Algebra U(osp(1,2)), XXVI International Workshop on Geometical Methods in Physics, (2007) , 175-179, American Institute of Physics
BiBTeX
@INPROCEEDINGS{Burdik07:140,
  title = {{Structure of the Enveloping Algebra U(osp(1,2))}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  address = {Melville, New York},
  booktitle = {{XXVI International Workshop on Geometical Methods in Physics}},
  publisher = {American Institute of Physics},
  year = {2007},
  volume = {1},
  pages = {175--179}
}

2006

Burdík, Č. and Navrátil, O. and Pošta, S., Matrix Solvable Calogero Models of G2 Type, Quantum Theory and Symmetries, (2006) , 596-599, Heron Press
BiBTeX
@INPROCEEDINGS{Burdik06:125,
  title = {{Matrix Solvable Calogero Models of G2 Type}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  address = {Sofia},
  booktitle = {{Quantum Theory and Symmetries}},
  publisher = {Heron Press},
  year = {2006},
  pages = {596--599}
}

2004

Burdík, Č. and Pogosyan, G., Two-Exactly-Solvable Broblems in One-Dimensional Hyperbolic Space, Proceedings of the 5th International Workshop Lie Theoru and Its Applications in Physics, (2004) , 294-300, World Scientific
BiBTeX
@INPROCEEDINGS{Burdik04:105,
  title = {{Two-Exactly-Solvable Broblems in One-Dimensional Hyperbolic Space}},
  author = {Burd{\'\i}k, {\v C}. and Pogosyan, G.},
  address = {Singapore},
  booktitle = {{Proceedings of the 5th International Workshop Lie Theoru and Its Applications in Physics}},
  publisher = {World Scientific},
  year = {2004},
  pages = {294--300}
}
Burdík, Č. and Navrátil, O., The q-boson-fermion realizations of quantum superalgebra U_q(gl(2,1)), Supersymmetries and Quantum Symmetries, (2004) , 174-180, JINR
BiBTeX
@INPROCEEDINGS{Burdik04:105,
  title = {{The q-boson-fermion realizations of quantum superalgebra U_q(gl(2,1))}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Dubna},
  booktitle = {{Supersymmetries and Quantum Symmetries}},
  publisher = {JINR},
  year = {2004},
  pages = {174--180}
}
Burdík, Č. and Navrátil, O., The q-boso-fermion realizations of quantum superalgebra U_q(gl(m,n)), Proceedings of the 5th International Workshop Lie Theoru and Its Applications in Physics, (2004) , 403-413, World Scientific
BiBTeX
@INPROCEEDINGS{Burdik04:105,
  title = {{The q-boso-fermion realizations of quantum superalgebra U_q(gl(m,n))}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Singapore},
  booktitle = {{Proceedings of the 5th International Workshop Lie Theoru and Its Applications in Physics}},
  publisher = {World Scientific},
  year = {2004},
  pages = {403--413}
}

2003

Tolar, J. and Beneš, M. and Burdík, Č. and Chadzitaskos, G. and Gemperle, F. and Havlíček, M. and Hlavatý, L. and Jex, I. and Pelantová, E. and Svoboda, V. and Šťovíček, P., Mathematical Methods in the Physics of Microworld, Proceedings of Workshop 2003, (2003) , 74-75, CTU
BiBTeX
@INPROCEEDINGS{Tolar03:8597,
  title = {{Mathematical Methods in the Physics of Microworld}},
  author = {Tolar, J. and Bene{\v s}, M. and Burd{\'\i}k, {\v C}. and Chadzitaskos, G. and Gemperle, F. and Havl{\'\i}{\v c}ek, M. and Hlavat{\' y}, L. and Jex, I. and Pelantov{\' a}, E. and Svoboda, V. and {\v S}{\v t}ov{\'\i}{\v c}ek, P.},
  address = {Prague},
  booktitle = {{Proceedings of Workshop 2003}},
  publisher = {CTU},
  year = {2003},
  volume = {A},
  pages = {74--75}
}
Burdík, Č. and Navrátil, O., Q-Boson Realizations of the Quantum Algebras, GROUP 24 : PHYSICAL AND MATHEMATICAL ASPECTS OF SYMMETRIES, (2003) , 795-798, Institute of Physics Publishing
BiBTeX
@INPROCEEDINGS{Burdik03:105,
  title = {{Q-Boson Realizations of the Quantum Algebras}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Bristol},
  booktitle = {{GROUP 24 : PHYSICAL AND MATHEMATICAL ASPECTS OF SYMMETRIES}},
  publisher = {Institute of Physics Publishing},
  year = {2003},
  pages = {795--798}
}
Burdík, Č. and Havlíček, M., Boson Realizations of Semi-simple Lie Algebras, Symmetry in Physics, (2003) , 101-112, American Mathematical Society
BiBTeX
@INPROCEEDINGS{Burdik03:942,
  title = {{Boson Realizations of Semi-simple Lie Algebras}},
  author = {Burd{\'\i}k, {\v C}. and Havl{\'\i}{\v c}ek, M.},
  address = {New York},
  booktitle = {{Symmetry in Physics}},
  publisher = {American Mathematical Society},
  year = {2003},
  pages = {101--112}
}

2002

Tolar, J. and Beneš, M. and Burdík, Č. and Chadzitaskos, G. and Gemperle, F. and Havlíček, M. and Hlavatý, L. and Jex, I. and Pelantová, E. and Svoboda, V. and Šťovíček, P., Mathematical Methods in the Physics of Microworld, Proceedings of Workshop 2002, (2002) , 80-81, CTU
BiBTeX
@INPROCEEDINGS{Tolar02:7357,
  title = {{Mathematical Methods in the Physics of Microworld}},
  author = {Tolar, J. and Bene{\v s}, M. and Burd{\'\i}k, {\v C}. and Chadzitaskos, G. and Gemperle, F. and Havl{\'\i}{\v c}ek, M. and Hlavat{\' y}, L. and Jex, I. and Pelantov{\' a}, E. and Svoboda, V. and {\v S}{\v t}ov{\'\i}{\v c}ek, P.},
  address = {Prague},
  booktitle = {{Proceedings of Workshop 2002}},
  publisher = {CTU},
  year = {2002},
  volume = {A},
  pages = {80--81}
}
Burdík, Č. and Navrátil, O. and Pashnev, A., On the Fock space realizations of nonlinear algebras describing the high spin fields in AdS spaces, Proceedings of 16th Born Symposium Supersymmetries and Quantum Symmetries, (2002) , 11-17, JINR
BiBTeX
@INPROCEEDINGS{Burdik02:808,
  title = {{On the Fock space realizations of nonlinear algebras describing the high spin fields in AdS spaces}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Pashnev, A.},
  address = {Dubna},
  booktitle = {{Proceedings of 16th Born Symposium Supersymmetries and Quantum Symmetries}},
  publisher = {JINR},
  year = {2002},
  pages = {11--17}
}

2001

Tolar, J. and Burdík, Č. and Chadzitaskos, G. and Gemperle, F. and Havlíček, M. and Hlavatý, L. and Jex, I. and Pelantová, E. and Šťovíček, P., Mathematical Methods in the Physics of Microworld, Proceedings of Workshop 2001, (2001) , 90-91, CTU
BiBTeX
@INPROCEEDINGS{Tolar01:6769,
  title = {{Mathematical Methods in the Physics of Microworld}},
  author = {Tolar, J. and Burd{\'\i}k, {\v C}. and Chadzitaskos, G. and Gemperle, F. and Havl{\'\i}{\v c}ek, M. and Hlavat{\' y}, L. and Jex, I. and Pelantov{\' a}, E. and {\v S}{\v t}ov{\'\i}{\v c}ek, P.},
  address = {Prague},
  booktitle = {{Proceedings of Workshop 2001}},
  publisher = {CTU},
  year = {2001},
  volume = {A},
  pages = {90--91}
}
Burdík, Č. and Pashnev, A. and Tsulaia, M., On the Mixed Symmetry Irreducible Representations of the Poincare Group in the BRST Approach, Supersymmetry and Quantum Field Theory, (2001) , 285-292, North Holland
BiBTeX
@INPROCEEDINGS{Burdik01:713,
  title = {{On the Mixed Symmetry Irreducible Representations of the Poincare Group in the BRST Approach}},
  author = {Burd{\'\i}k, {\v C}. and Pashnev, A. and Tsulaia, M.},
  address = {Budapest},
  booktitle = {{Supersymmetry and Quantum Field Theory}},
  publisher = {North Holland},
  year = {2001},
  volume = {1},
  pages = {285--292}
}
Burdík, Č. and King, A. and Welsh, B., The Explicit Construction of Irreducible Representations of the Quantum Algebra Uq(sl(n)), NEW DEVELOPMENTS IN FUNDAMENTAL INTERACTION THEORIES, (2001) , 158-169, American Institute of Physics
BiBTeX
@INPROCEEDINGS{Burdik01:707,
  title = {{The Explicit Construction of Irreducible Representations of the Quantum Algebra Uq(sl(n))}},
  author = {Burd{\'\i}k, {\v C}. and King, A. and Welsh, B.},
  address = {Philadelphia},
  booktitle = {{NEW DEVELOPMENTS IN FUNDAMENTAL INTERACTION THEORIES}},
  publisher = {American Institute of Physics},
  year = {2001},
  pages = {158--169}
}

2000

Tolar, J. and Beneš, M. and Burdík, Č. and Gemperle, F. and Havlíček, M. and Hlavatý, L. and Chadzitaskos, G. and Jex, I. and Kůs, V. and Pelantová, E. and Šťovíček, P., Mathematical Methods in the Physics of Microworld, Proceedings of Workshop 2000, (2000) , 63, CTU
BiBTeX
@INPROCEEDINGS{Tolar00:3917,
  title = {{Mathematical Methods in the Physics of Microworld}},
  author = {Tolar, J. and Bene{\v s}, M. and Burd{\'\i}k, {\v C}. and Gemperle, F. and Havl{\'\i}{\v c}ek, M. and Hlavat{\' y}, L. and Chadzitaskos, G. and Jex, I. and K{\r u}s, V. and Pelantov{\' a}, E. and {\v S}{\v t}ov{\'\i}{\v c}ek, P.},
  address = {Prague},
  booktitle = {{Proceedings of Workshop 2000}},
  publisher = {CTU},
  year = {2000},
  volume = {A},
  pages = {63}
}
Burdík, Č. and Navrátil, O., New q-Boson Realizations of the Quantum Groups Uq(C3), New Symmetries and Integrable Models, (2000) , 19-26, World Scientific
BiBTeX
@INPROCEEDINGS{Burdik00:378,
  title = {{New q-Boson Realizations of the Quantum Groups Uq(C3)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Singapore},
  booktitle = {{New Symmetries and Integrable Models}},
  publisher = {World Scientific},
  year = {2000},
  pages = {19--26}
}
Burdík, Č. and Navrátil, O., New q-Boson Realizations of the Quantum Groups UqA(n), Supersymmetries and Quantum Symmetries, (2000) , 351-357, Joint Institute for Nuclear Research
BiBTeX
@INPROCEEDINGS{Burdik00:379,
  title = {{New q-Boson Realizations of the Quantum Groups UqA(n)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Dubna},
  booktitle = {{Supersymmetries and Quantum Symmetries}},
  publisher = {Joint Institute for Nuclear Research},
  year = {2000},
  pages = {351--357}
}
Burdík, Č. and Navrátil, O., New q-Boson Realizations of the Quantum Groups U_q(A_n), Supersymmetries and Quantum Symmetries, (2000) , 351-357, Joint Institute for Nuclear Research
BiBTeX
@INPROCEEDINGS{Burdik00:400,
  title = {{New q-Boson Realizations of the Quantum Groups U_q(A_n)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Dubna},
  booktitle = {{Supersymmetries and Quantum Symmetries}},
  publisher = {Joint Institute for Nuclear Research},
  year = {2000},
  pages = {351--357}
}
Burdík, Č. and Navrátil, O., New Boson Realizations of the Quantum Groups UqA(n), The Proceeding of the 19th Winter School Geometry and Physics, (2000) , 9-15, Univerzita Karlova, Matematicko-fyzikální fakulta
BiBTeX
@INPROCEEDINGS{Burdik00:378,
  title = {{New Boson Realizations of the Quantum Groups UqA(n)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Praha},
  booktitle = {{The Proceeding of the 19th Winter School Geometry and Physics}},
  publisher = {Univerzita Karlova, Matematicko-fyzik{\' a}ln{\'\i} fakulta},
  year = {2000},
  pages = {9--15}
}
Burdík, Č. and Navrátil, O., New Boson Realizations of Quantum Groups U_q (A_n), Geometry and Physics, (2000) , 75-84, Direzione e Redazione
BiBTeX
@INPROCEEDINGS{Burdik00:400,
  title = {{New Boson Realizations of Quantum Groups U_q (A_n)}},
  author = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  address = {Palermo},
  booktitle = {{Geometry and Physics}},
  publisher = {Direzione e Redazione},
  year = {2000},
  pages = {75--84}
}

1999

Tolar, J. and Burdík, Č. and Chadzitaskos, G. and Havlíček, M. and Hlavatý, L. and Jex, I. and Pelantová, E. and Šťovíček, P., Rigorous Models of Intergrable and Chaotic Systems, CTU Reports, Vol. 3, No. 1, (1999) , 80, CTU
BiBTeX
@INPROCEEDINGS{Tolar99:3918,
  title = {{Rigorous Models of Intergrable and Chaotic Systems}},
  author = {Tolar, J. and Burd{\'\i}k, {\v C}. and Chadzitaskos, G. and Havl{\'\i}{\v c}ek, M. and Hlavat{\' y}, L. and Jex, I. and Pelantov{\' a}, E. and {\v S}{\v t}ov{\'\i}{\v c}ek, P.},
  address = {Prague},
  booktitle = {{CTU Reports, Vol. 3, No. 1}},
  publisher = {CTU},
  year = {1999},
  pages = {80}
}

1998

Burdík, Č. and Chadzitaskos, G. and Dittrich, J. and Exner, P. and Havlíček, M. and Hlavatý, L. and Jex, I. and Pelantová, E. and Šeba, P. and Šťovíček, P. and Tater, M. and Tolar, J. and Znojil, M., Rigorous Models of Integrable and Chaotic Quantum Systems, Workshop 98, (1998) , 51-52, CTU
BiBTeX
@INPROCEEDINGS{Burdik98:576,
  title = {{Rigorous Models of Integrable and Chaotic Quantum Systems}},
  author = {Burd{\'\i}k, {\v C}. and Chadzitaskos, G. and Dittrich, J. and Exner, P. and Havl{\'\i}{\v c}ek, M. and Hlavat{\' y}, L. and Jex, I. and Pelantov{\' a}, E. and {\v S}eba, P. and {\v S}{\v t}ov{\'\i}{\v c}ek, P. and Tater, M. and Tolar, J. and Znojil, M.},
  address = {Prague},
  booktitle = {{Workshop 98}},
  publisher = {CTU},
  year = {1998},
  volume = {I},
  pages = {51--52}
}

1995

Havlíček, M. and Burdík, Č. and Hlavatý, L. and Šťovíček, P. and Tolar, J., Quantum Symmetries: Mathematical Models and Physical Applications, Workshop 95, (1995) , 97-98, CTU
BiBTeX
@INPROCEEDINGS{Havlicek95:4,
  title = {{Quantum Symmetries: Mathematical Models and Physical Applications}},
  author = {Havl{\'\i}{\v c}ek, M. and Burd{\'\i}k, {\v C}. and Hlavat{\' y}, L. and {\v S}{\v t}ov{\'\i}{\v c}ek, P. and Tolar, J.},
  address = {Prague},
  booktitle = {{Workshop 95}},
  publisher = {CTU},
  year = {1995},
  volume = {I},
  pages = {97--98}
}

1994

Tolar, J. and Havlíček, M. and Hlavatý, L. and Šťovíček, P. and Burdík, Č., Nonlinear Models in Quantum Physics, CTU Seminar 94, (1994) , 123-124, CTU
BiBTeX
@INPROCEEDINGS{Tolar94:3979,
  title = {{Nonlinear Models in Quantum Physics}},
  author = {Tolar, J. and Havl{\'\i}{\v c}ek, M. and Hlavat{\' y}, L. and {\v S}{\v t}ov{\'\i}{\v c}ek, P. and Burd{\'\i}k, {\v C}.},
  address = {Prague},
  booktitle = {{CTU Seminar 94}},
  publisher = {CTU},
  year = {1994},
  pages = {123--124}
}

1993

Tolar, J. and Havlíček, M. and Šťovíček, P. and Burdík, Č., Nonlinear Models in Quantum Physics, Workshop 93, (1993) , 97-98, CTU
BiBTeX
@INPROCEEDINGS{Tolar93:3895,
  title = {{Nonlinear Models in Quantum Physics}},
  author = {Tolar, J. and Havl{\'\i}{\v c}ek, M. and {\v S}{\v t}ov{\'\i}{\v c}ek, P. and Burd{\'\i}k, {\v C}.},
  address = {Prague},
  booktitle = {{Workshop 93}},
  publisher = {CTU},
  year = {1993},
  pages = {97--98}
}
Burdík, Č. and King, R. and Welsh, T.A., The Explicit Construction of Irreducible Representations of the Quantum Group, 3rd Wigner Symposium, Sept. 1993, (1993) , -,
BiBTeX
@INPROCEEDINGS{Burdik93:429,
  title = {{The Explicit Construction of Irreducible Representations of the Quantum Group}},
  author = {Burd{\'\i}k, {\v C}. and King, R. and Welsh, T.A.},
  address = {Oxford},
  booktitle = {{3rd Wigner Symposium, Sept. 1993}},
  year = {1993},
  pages = {--}
}

2013

Burdík, Č. and Navrátil, O. and Pošta, S. (ed.), XXth International Conference on Integrable Systems and Quantum Symmetries (ISQS-20), 17-23 June 2012, Prague, Czech Republic, (2013) , Institute of Physics Publishing
BiBTeX
@PROCEEDINGS{Burdik13:217,
  title = {{XXth International Conference on Integrable Systems and Quantum Symmetries (ISQS-20), 17-23 June 2012, Prague, Czech Republic}},
  address = {Bristol},
  editor = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  publisher = {Institute of Physics Publishing},
  year = {2013}
}

2012

Burdík, Č. and Navrátil, O. and Pošta, S. and Schnabl, M. and Šnobl, L. (ed.), 7th International Conference on Quantum Theory and Symmetries (QTS7) 7-13 August 2011, Prague, Czech Republic, (2012) , Institute of Physics Publishing
BiBTeX
@PROCEEDINGS{Burdik12:189,
  title = {{7th International Conference on Quantum Theory and Symmetries (QTS7) 7-13 August 2011, Prague, Czech Republic}},
  address = {Bristol},
  editor = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S. and Schnabl, M. and {\v S}nobl, L.},
  publisher = {Institute of Physics Publishing},
  year = {2012}
}

2008

Burdík, Č. and Navrátil, O. and Pošta, S. (ed.), Advanced Summer School on Integrable Systems and Quantum Symmetries, (2008) , 56, CTU Publishing House
BiBTeX
@PROCEEDINGS{Burdik08:149,
  title = {{Advanced Summer School on Integrable Systems and Quantum Symmetries}},
  address = {Praha},
  editor = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  publisher = {CTU Publishing House},
  year = {2008},
  pages = {56}
}
Burdík, Č. and Mrugala, R. and Popowicz, Z. (ed.), XVIth International Colloquium on Integrable Systems and Quantum Symmetries, (2008) , 238, Pergamon Press
BiBTeX
@PROCEEDINGS{Burdik08:149,
  title = {{XVIth International Colloquium on Integrable Systems and Quantum Symmetries}},
  address = {Oxford},
  editor = {Burd{\'\i}k, {\v C}. and Mrugala, R. and Popowicz, Z.},
  publisher = {Pergamon Press},
  year = {2008},
  pages = {238}
}

2006

Burdík, Č. and Pošta, S. and Navrátil, O. (ed.), Proceedings of the 15th International Colloquium on Quantum Groups, (2006) , 241, Springer
BiBTeX
@PROCEEDINGS{Burdik06:125,
  title = {{Proceedings of the 15th International Colloquium on Quantum Groups}},
  address = {New York},
  editor = {Burd{\'\i}k, {\v C}. and Po{\v s}ta, S. and Navr{\' a}til, O.},
  publisher = {Springer},
  year = {2006},
  pages = {241}
}

2005

Burdík, Č. and Navrátil, O. and Pošta, S. (ed.), The 8th International Conference Path Integrals from Quantum Information to Cosmology, (2005) , 21, JINR
BiBTeX
@PROCEEDINGS{Burdik05:116,
  title = {{The 8th International Conference Path Integrals from Quantum Information to Cosmology}},
  address = {Dubna},
  editor = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  publisher = {JINR},
  year = {2005},
  pages = {21}
}
Burdík, Č. and Navrátil, O. and Pošta, S. (ed.), Papers of the 14-th International Colloquium Quantum Groups, (2005) , 246, Kluwer Press
BiBTeX
@PROCEEDINGS{Burdik05:116,
  title = {{Papers of the 14-th International Colloquium Quantum Groups}},
  address = {New York},
  editor = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  publisher = {Kluwer Press},
  year = {2005},
  pages = {246}
}

2004

Burdík, Č. and Navrátil, O. and Pošta, S. (ed.), Proceedings of International Conference Symmetry Methods in Physics, (2004) , 28, JINR
BiBTeX
@PROCEEDINGS{Burdik04:105,
  title = {{Proceedings of International Conference Symmetry Methods in Physics}},
  address = {Dubna},
  editor = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O. and Po{\v s}ta, S.},
  publisher = {JINR},
  year = {2004},
  pages = {28}
}
Burdík, Č. and Navrátil, O. (ed.), Papers of the 13-th International Colloquium Quantum Groups, (2004) , 270, Kluwer Press
BiBTeX
@PROCEEDINGS{Burdik04:105,
  title = {{Papers of the 13-th International Colloquium Quantum Groups}},
  address = {New York},
  editor = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  publisher = {Kluwer Press},
  year = {2004},
  pages = {270}
}

2003

Burdík, Č. and Navrátil, O. (ed.), Papers of the 12th International Colloquium on Quantum Groups, (2003) , 250, Academy of Sciences of the Czech Republic, Institute of Physics
BiBTeX
@PROCEEDINGS{Burdik03:941,
  title = {{Papers of the 12th International Colloquium on Quantum Groups}},
  address = {Prague},
  editor = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  publisher = {Academy of Sciences of the Czech Republic, Institute of Physics},
  year = {2003},
  pages = {250}
}

2002

Burdík, Č. and Navrátil, O. (ed.), Papers of the 11-th International Colloquium on Quantum Groups, (2002) , 127, Academy of Sciences of the Czech Republic, Institute of Physics
BiBTeX
@PROCEEDINGS{Burdik02:807,
  title = {{Papers of the 11-th International Colloquium on Quantum Groups}},
  address = {Prague},
  editor = {Burd{\'\i}k, {\v C}. and Navr{\' a}til, O.},
  publisher = {Academy of Sciences of the Czech Republic, Institute of Physics},
  year = {2002},
  pages = {127}
}

2001

Burdík, Č. (ed.), Papers of the 10th International Colloquium on Quantum Groups, (2001) , 222, Academy of Sciences of the Czech Republic, Institute of Physics
BiBTeX
@PROCEEDINGS{Burdik01:717,
  title = {{Papers of the 10th International Colloquium on Quantum Groups}},
  address = {Prague},
  editor = {Burd{\'\i}k, {\v C}.},
  publisher = {Academy of Sciences of the Czech Republic, Institute of Physics},
  year = {2001},
  pages = {222}
}

2000

Burdík, Č. (ed.), Papers of the 9th International Colloquium on Quantum Groups, (2000) , 199, Academy of Sciences of the Czech Republic, Institute of Physics
BiBTeX
@PROCEEDINGS{Burdik00:363,
  title = {{Papers of the 9th International Colloquium on Quantum Groups}},
  address = {Prague},
  editor = {Burd{\'\i}k, {\v C}.},
  publisher = {Academy of Sciences of the Czech Republic, Institute of Physics},
  year = {2000},
  pages = {199}
}
Burdík, Č. (ed.), Papers of the 8th International Colloquium on Quantum Groups, (2000) , 224, Academy of Sciences of the Czech Republic, Institute of Physics
BiBTeX
@PROCEEDINGS{Burdik00:363,
  title = {{Papers of the 8th International Colloquium on Quantum Groups}},
  address = {Prague},
  editor = {Burd{\'\i}k, {\v C}.},
  publisher = {Academy of Sciences of the Czech Republic, Institute of Physics},
  year = {2000},
  pages = {224}
}

Ostatní publikace

1999

Burdík, Č., Q-boson Realization of Quantum Groups, 1999
BiBTeX
@UNPUBLISHED{Burdik99:254,
  title = {{Q-boson Realization of Quantum Groups}},
  author = {Burd{\'\i}k, {\v C}.},
  year = {1999},
  note = {Unpublished Lecture}
}
Burdík, Č., Q-boson Realization of Quantum Groups, 1999
BiBTeX
@UNPUBLISHED{Burdik99:252,
  title = {{Q-boson Realization of Quantum Groups}},
  author = {Burd{\'\i}k, {\v C}.},
  year = {1999},
  note = {Unpublished Lecture}
}
Burdík, Č., Matematické modely kvazikrystalů, 1999
BiBTeX
@UNPUBLISHED{Burdik99:254,
  title = {{Matematick{\' e} modely kvazikrystal{\r u}}},
  author = {Burd{\'\i}k, {\v C}.},
  year = {1999},
  note = {Unpublished Lecture}
}
Burdík, Č., New Boson Realizations of Quantum Groups Uq(An), 1999
BiBTeX
@UNPUBLISHED{Burdik99:254,
  title = {{New Boson Realizations of Quantum Groups Uq(An)}},
  author = {Burd{\'\i}k, {\v C}.},
  year = {1999},
  note = {Unpublished Lecture}
}
Burdík, Č., Boson Realization of Quantum Groups and Supergroups, 1999
BiBTeX
@UNPUBLISHED{Burdik99:254,
  title = {{Boson Realization of Quantum Groups and Supergroups}},
  author = {Burd{\'\i}k, {\v C}.},
  year = {1999},
  note = {Unpublished Lecture}
}

1998

Burdík, Č., Properties of quasicrystals, 1998
BiBTeX
@UNPUBLISHED{Burdik98:254,
  title = {{Properties of quasicrystals}},
  author = {Burd{\'\i}k, {\v C}.},
  year = {1998},
  note = {Unpublished Lecture}
}
Burdík, Č. (ed.), Quantum Groups and Integrable Systems 1998, (1998) , 255, Academy of Sciences of the Czech Republic, Institute of Physics
BiBTeX
@PROCEEDINGS{Burdik98:252,
  title = {{Quantum Groups and Integrable Systems 1998}},
  address = {Prague},
  editor = {Burd{\'\i}k, {\v C}.},
  publisher = {Academy of Sciences of the Czech Republic, Institute of Physics},
  year = {1998},
  pages = {255}
}

1997

Burdík, Č., Universal R-matrix for nonstandard deformation of Uq(so(3)), 1997
BiBTeX
@UNPUBLISHED{Burdik97:254,
  title = {{Universal R-matrix for nonstandard deformation of Uq(so(3))}},
  author = {Burd{\'\i}k, {\v C}.},
  year = {1997},
  note = {Unpublished Lecture}
}

Gaudinovy modely

školitel: Čestmír Burdík
e-mail: zobrazit e-mail
typ práce: bakalářská práce, diplomová práce
zaměření: MI_MM
klíčová slova: Gaudin model, Bethe Ansatz
odkaz: http://kmlinux.fjfi.cvut.cz/~burdik/research/gaudin.pdf
popis: Matematické téma z teorie matic. Jedná se o hledání vlastních vektorů a vlastních čísel. Předpokládá studium teorie reprezentací nekonečně dimensinálních Lieových algeber atd. Bliže je možné se seznámit v nedavné publikaci školitele: http://babbage.sissa.it/PS_cache/arxiv/pdf/0805/0805.4495v1.pdf a prednašce prof. A. Varchenka http://video.google.com/videoplay?docid=7771443320464067554 Téma má návaznost na Langlandsův program: http://en.wikipedia.org/wiki/Langlands_program
literatura: http://kmlinux.fjfi.cvut.cz/~burdik/research/lit.pdf
poznámka: K vypracování konkretního zadání je nutná osobní konzultace se školitelem
naposledy změněno: 16.09.2011 08:15:35

Kvantové grupy a kvantové spinové řetízky

školitel: prof. RNDr. Čestmír Burdík, DrSc.
e-mail: zobrazit e-mail
typ práce: dizertační práce
zaměření: MI_MM
klíčová slova: kvantové grupy, Hecke algebra, Birman-Murakami-Wenzl algebra, kvantový spinový řetízek
odkaz: http://km.fjfi.cvut.cz/intsystems/
popis: Kvantové grupy[1] hrají v matematické fyzice důležitou roli při studiu spinových řetízků. Plánujeme vyšetřovat modely spinových řetízků s netriviálními okrajovými podmínkami, které jsou formulovány pomoci reprezentací Hecke algeber , Birman-Murakami-Wenzl algeber [2] a fermionů [3].
literatura: [1] A. Klimyk and K. Schmudgen,Quantum Groups and Their Representations, Springer, Berlin, 1997 [2] C.Burdik, A.P.Isaev, O.Ogievetsky,{\\it Standard Complex for Quantum Lie Algebras} Yad. Phys. {\\bf 64} N0. 12 (2001) 2191; {QA/0010060}. [3] C. Burdik, A. P. Isaev, S.O. Krivonos and O. Navratil, Spin chain models, Hecke algebras and free fermions, in preparation.
poznámka: K vypracování konkretního zadání je nutná osobní konzultace se školitelem.
naposledy změněno: 27.03.2013 10:17:28

Supersymetrická mechanika a integrabilita.

školitel: prof. RNDr. Čestmír Burdík, DrSc.
e-mail: zobrazit e-mail
typ práce: dizertační práce
zaměření: MI_MM
klíčová slova: supersymetrická mechanika, supermultiplet, $CP^n$ varieta, Hamiltonián
odkaz: http://km.fjfi.cvut.cz/intsystems/
přiložený soubor: ikona pdf
popis: Zajímavým problémem v supersymetrické mechanice[1] souvisejícím s teorií reprezentaci je studiu supersymetrických integrabilních modelů. Nedávno [2] jsme navrhli zobecněné nelineární chirální super-multiplet, který je definován pomocí 2n bosonových super-polí které splňují nelineárních vazby. Základem byla jeho invariance působení SU (n + 1) grupy. Tento systém popisuje pohyb částice nad $CP ^ n $ varietě. Nyní plánujeme studovat tento systém podrobněji. Hlavní otázka, kterou se chystáme odpovědět, je konstrukce kompletního Hamiltoniánu.
literatura: [1]Supersymmetric Mechanics in Superspace S. Bellucci, S. Krivonos Journal-ref: Lect.Notes Phys.698:49-96,2006 [2] C. Burdik, S. Krivonos, A. Sutulin, Generalized non-linear chiral supermultiplets, Journal of Physics Conference Series Volume: 343 Article Number: 012119 DOI: 10.1088/1742-6596/343/1/012119, Published: 2012, ISSN 1742-6588.
poznámka: K vypracování konkretního zadání je nutná osobní konzultace se školitelem.
naposledy změněno: 26.03.2013 17:34:48

za obsah této stránky zodpovídá: Radek Fučík | naposledy změněno: 7.8.2011
Trojanova 13, 120 00 Praha 2, tel. 224 358 540, pevná linka 224 923 098, fax 234 358 643
České vysoké učení technické v Praze | Fakulta jaderná a fyzikálně inženýrská | Katedra matematiky