Universität Wien

250123 VO Gauge Theory, Lagrangians, and Symmetries (2024W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
MIXED
Moodle
Mo 25.11. 16:45-18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

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Details

Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 01.10. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.10. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 08.10. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.10. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 15.10. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.10. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 22.10. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.10. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 29.10. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 04.11. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.11. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 11.11. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.11. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 18.11. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.11. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 26.11. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 02.12. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 03.12. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 09.12. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.12. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 16.12. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.12. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 07.01. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 13.01. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.01. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 20.01. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.01. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 27.01. 16:45 - 18:15 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.01. 15:00 - 16:30 Seminarraum 12 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The aim of this course is to provide the background for some fundamental geometric and algebraic concepts underlying basic constructions in the Standard Model of Particle Physics. The lectures will be based on selected material from Chapters 6-8 of Hamilton’s recent book [1], but we also offer detailed lecture notes at https://www.mat.univie.ac.at/~mike/GTLS.pdf

The key notions we plan to discuss are pseudo-orthogonal groups, Clifford algebras, spinor representations, spin groups, spin structures, spinor bundles, spin covariant derivatives, Dirac operators, Yang-Mills theory, gauge-invariant Lagrangians on associated vector bundles, symmetry breaking and Higgs mechanism.

Assessment and permitted materials

oral exam

Minimum requirements and assessment criteria

The prerequisites to follow the course are (a) a firm background in differential geometry and linear algebra along with (b) knowledge of Lie groups and principal fiber bundles comparable with the material in corresponding master courses from winter term 2023/24 and summer term 2024. For a successful exam, a thorough understanding of the definitions, results, and proofs has to be shown in detailed answers to questions.

Examination topics

As provided in the lecture notes.

Reading list

[1] Mark J.D. Hamilton: Mathematical Gauge Theory, Springer Universitext 2017.
- Additional references are included in the lecture notes
https://www.mat.univie.ac.at/~mike/GTLS.pdf

Association in the course directory

MGEV

Last modified: Mo 02.09.2024 11:46