Course: Geometric Methods in Physics II

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Course title Geometric Methods in Physics II
Course code MU/03053
Organizational form of instruction Lecture + Lesson
Level of course not specified
Year of study not specified
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
  • SERGYEYEV Artur, doc. RNDr. Ph.D.
Course content
- Foundations of the Riemannian geometry (manifolds, tensor fields, metric tensor, Lie derivative, Killing vectors, affine connection, curvature, torsion, geodesics) - Geometric methods in general relativity (variational principles in GR, some exact solutions of the Einstein equations) - Foundations of the Lie group theory and some of its applications in physics (Lie groups and Lie algebras and their relations, exponential map, foundations of the structural theory of Lie algebras and their representations, fiber bundles and connections on them, gauge fields, the Lagrangian and some exact solutions of the Yang-Mills equations)

Learning activities and teaching methods
Recommended literature
  • C. Isham. Modern Differential Geometry for Physicists. Singapore, 1999.
  • D. Krupka. Matematické základy OTR.
  • K. Erdmann, M. Wildon. Introduction to Lie algebras. Springer, 2006.
  • L.H. Ryder. Quantum Field Theory. 1996.
  • M. Fecko. Diferenciálna geometria a Lieove grupy pre fyzikov. Bratislava, Iris, 2004.
  • M. Nakahara. Geometry, Topology and Physics. Institute of Physics Publishing, 1990.
  • O. Kowalski. Úvod do Riemannovy geometrie. Univerzita Karlova, Praha, 1995.
  • S. Caroll. Lecture Notes on General Relativity.

Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester