Universität Wien
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250043 VO Gauge theory, Lagrangians, and Symmetries (2020W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Thursday 01.10. 09:30 - 11:00 Digital
  • Tuesday 06.10. 09:30 - 11:00 Digital
  • Thursday 08.10. 09:30 - 11:00 Digital
  • Tuesday 13.10. 09:30 - 11:00 Digital
  • Thursday 15.10. 09:30 - 11:00 Digital
  • Tuesday 20.10. 09:30 - 11:00 Digital
  • Thursday 22.10. 09:30 - 11:00 Digital
  • Tuesday 27.10. 09:30 - 11:00 Digital
  • Thursday 29.10. 09:30 - 11:00 Digital
  • Tuesday 03.11. 09:30 - 11:00 Digital
  • Thursday 05.11. 09:30 - 11:00 Digital
  • Tuesday 10.11. 09:30 - 11:00 Digital
  • Thursday 12.11. 09:30 - 11:00 Digital
  • Tuesday 17.11. 09:30 - 11:00 Digital
  • Thursday 19.11. 09:30 - 11:00 Digital
  • Tuesday 24.11. 09:30 - 11:00 Digital
  • Thursday 26.11. 09:30 - 11:00 Digital
  • Tuesday 01.12. 09:30 - 11:00 Digital
  • Thursday 03.12. 09:30 - 11:00 Digital
  • Thursday 10.12. 09:30 - 11:00 Digital
  • Tuesday 15.12. 09:30 - 11:00 Digital
  • Thursday 17.12. 09:30 - 11:00 Digital
  • Thursday 07.01. 09:30 - 11:00 Digital
  • Tuesday 12.01. 09:30 - 11:00 Digital
  • Thursday 14.01. 09:30 - 11:00 Digital
  • Tuesday 19.01. 09:30 - 11:00 Digital
  • Thursday 21.01. 09:30 - 11:00 Digital
  • Tuesday 26.01. 09:30 - 11:00 Digital
  • Thursday 28.01. 09:30 - 11:00 Digital

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/teaching/ws2021/LNGHMK.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

(Digital) 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 2019/20 and summer term 2020. 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/teaching/ws2021/LNGHMK.pdf

Association in the course directory

MGEV

Last modified: Fr 17.05.2024 00:14