MU03053 Geometric Methods in Physics II

Mathematical Institute in Opava
Summer 2009
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Kristína Smítalová, CSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU03052 Geometric Methods in Phys. I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
there are 7 fields of study the course is directly associated with, display
Course objectives (in Czech)
Moderní geometrické metody matematické fyziky v mechanice, teorii relativity a teorii pole.
Syllabus (in Czech)
  • - Integrační metody pro řešení variačních rovnic v mechanice (dynamická distribuce, vztah mezi symetriemi Lagrangiánu, Eulerovy-Lagrangeovy formy, Lepageovy formy a symetriemi dynamické distribuce, Frobeniova věta, první integrály, Dabouxova věta, úplný integrál a Hamiltonova-Jacobiho rovnice, kanonické transformace)
    - Geometrické metody v obecné teorii relativity (topologické variety, Lorentzovské variety, globální a kausální struktura, variační principy OTR, řešení Einsteinových rovnic)
    - Geometrické metody v teorii pole (Lieovy grupy a algebry, reprezentace variační metody v teorii pole, skalární vektorová a spinorova pole, symetrie a první integrály)
Literature
    recommended literature
  • D. Krupka. Matematické základy OTR. info
  • O. Krupková. The Geometry of Variational ODE. Lecture Notes in Mathematics 1678, Springer, 1997. info
  • M. Nakahara. Geometry, Topology and Physics. Institute of Physics Publishing, 1990. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019.
  • Enrolment Statistics (Summer 2009, recent)
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