MU:MU03053 Geometric Methods in Phys. II - Course Information
MU03053 Geometric Methods in Physics II
Mathematical Institute in OpavaSummer 2012
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Guaranteed by
- prof. RNDr. Artur Sergyeyev, Ph.D., DSc.
Mathematical Institute in Opava - Prerequisites
- 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
- Geometry (programme MU, M1101)
- Geometry (programme MU, N1101)
- Mathematical Analysis (programme MU, M1101)
- Mathematical Analysis (programme MU, N1101)
- Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
- Secondary School Teacher Training in Mathematics (programme FPF, M7504)
- Course objectives
- Modern geometrical methods of mathematical physics in mechanics, relativity and field theory.
- Syllabus
- - 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)
- - Foundations of the Riemannian geometry (manifolds, tensor fields, metric tensor, Lie derivative, Killing vectors, affine connection, curvature, torsion, geodesics)
- Literature
- recommended literature
- S. Caroll. Lecture Notes on General Relativity. URL info
- D. Krupka. Matematické základy OTR. info
- K. Erdmann, M. Wildon. Introduction to Lie algebras. Springer, 2006. info
- M. Fecko. Diferenciálna geometria a Lieove grupy pre fyzikov. Bratislava, Iris, 2004. info
- C. Isham. Modern Differential Geometry for Physicists. Singapore, 1999. info
- L.H. Ryder. Quantum Field Theory. 1996. info
- O. Kowalski. Úvod do Riemannovy geometrie. Univerzita Karlova, Praha, 1995. 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.
- Teacher's information
- Oral exam; further requirements to be specified in the course of the semester.
- Enrolment Statistics (Summer 2012, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2012/MU03053