MU:MU03053 Geometric Methods in Phys. II

MU03053 Geometric Methods in Physics II

Mathematical Institute in Opava
Summer 2019

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: zk (examination).

Guaranteed by

Prerequisites

MU03052 Geometric Methods in Phys. I

Course Enrolment Limitations

The course is offered to students of any study field.

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)

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.