MU03053 Geometric Methods in Physics II

Mathematical Institute in Opava
Summer 2016
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
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.
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 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2017, Summer 2018, Summer 2019.
  • Enrolment Statistics (Summer 2016, recent)
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