F8350 Metody diferenciální geometrie ve fyzice

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
0/2. 3 credit(s). Type of Completion: graded credit.
Teacher(s)
Mgr. Pavel Klepáč, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Mirko Černák, CSc.
Department of Plasma Physics and Technology – Physics Section – Faculty of Science
Contact Person: Mgr. Pavel Klepáč, Ph.D.
Prerequisites
(F3063 Itegration of forms || F6420 Integral and differential calculus on manifolds) && F4120 Theoretical mechanics && F4090 Electrodynamics and the relativity theory
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
Course objectives
The lecture is intended to become an advanced treatment of the standard university course in calculus on manifolds and its application in physics. The main motivation is an introduction to methods of modern differential geometry and in particular aquirement of this approach in practical problems of theoretical physics. An emphasis is placed on an ability of systematic use of various concepts coming from coordinate independent differential geometry.
Syllabus
  • 1. Riemann and pseudoriemann geometry on manifolds (metric, differential forms, non-holonomic basis, Cartan structure equations, covariant derivative, curvature and torsion, geodesics, Hodge theory, Lie algebras). 2. Application in physics (differential operators in curved coordinates, theoretical mechanics, continuum mechanics, electrodynamics, special and general relativity). 3. Connection on fibre bundles (holonomy, homology and cohomology, a basic introduction to characteristic classes). 4. Application of fibre bundles in physics (field theory, Yang-Mills theory, general relativity and alternative approaches to gravity, string theory).
Literature
  • CHERN, Shiing-Shen, Wei-huan CHEN and Kai Shue LAM. Lectures on differential geometry. Singapore: World Scientific, 1998, x, 356 s. ISBN 981-02-3494-5. info
  • NAKAHARA, Mikio. Geometry, topology and physics. Bristol: Institute of physics publishing, 1990, xiii, 505. ISBN 0-85274-095-6. info
  • KRUPKA, Demeter and Jana MUSILOVÁ. Integrální počet na euklidových prostorech a diferencovatelných varietách. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1982, 320 s. info
  • STRAUMANN, Norbert. General relativity and relativistic astrophysics. Berlin: Springer-Verlag, 1984, 13, 459. ISBN 3540130101. info
  • Volobuev I. P. and Kubyšin J. A., Differential geometry and Lie algebras and applications in field theory
Assessment methods (in Czech)
Klasifikovaný zápočet, interaktivní způsob vedení předmětu
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2006, Spring 2008.