F7550 Gauge groups and fields

Faculty of Science
Autumn 2018
Extent and Intensity
2/0/0. 2 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. Franz Hinterleitner, Ph.D. (lecturer)
Guaranteed by
prof. RNDr. Jana Musilová, CSc.
Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Contact Person: doc. Franz Hinterleitner, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics - Physics Section - Faculty of Science
Prerequisites
Electrodynamics, basic knowledge of manifolds
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
Symmetries, Lie groups and algebras, manifolds, bundles, gauge fields, like the electromagnetic or the Yang-Mills fields, in the framework of principle bundles of Lie groups and their connections and covariant derivatives. Uniform geometric description of gauge fields as bundle curvature, derived from the connection. Application to gravity. Aims: Geometric point of view of Lie groups and algebras; geometric understanding of gauge fields
Learning outcomes
After absolving the course the students
- know the principles of the theory of Lie groups and algebras, particularly SO(3) and the Lorentz group
- have s geometric insight into the theory of Lie groups and algebras, understand the meaning of metric and connection on various bundles
- understand the geometric nature of gauge theories
Syllabus
• Symmetries, Lie groups and algebras,
• manifolds, bundles,
• gauge fields, like the electrodynamic or the Yang-Mills field in the formalism of principle bundles of Lie groups and their connexions and covariant derivatives.
• Unified geometric description of gauge fields as bundle curvature, derived from a connexion.
• Application to gravity.
Literature
• NAKAHARA, Mikio. Geometry, topology and physics. Bristol: Institute of physics publishing, 1990. xiii, 505. ISBN 0-85274-095-6. info
Teaching methods
lectures
Assessment methods
oral exam
Language of instruction
Czech