Universität Wien
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520036 VU Geometry of Gauge theories: old and new (2024W)

1.50 ECTS (1.00 SWS), SPL 52 - Doktoratsstudium Physik
Prüfungsimmanente Lehrveranstaltung

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").

Details

max. 15 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine

Jeden Mittwoch von 11:00 - 12:45 (including 15 minutes break)
beginnend mit 16. Oktober bis inklusive 27. November 2024 am ESI, Vienna, Schrödinger Lecture Hall, Boltzmanngasse 9, 1090 Vienna


Information

Ziele, Inhalte und Methode der Lehrveranstaltung

This course aims at introducing students to some of the geometry of modern gauge theories. We start with a concise overview of the standard setting: principal and associated bundles, connections, curvature and how they appear in the standard model of particle physics and in Einstein gravity. We then introduce Lie algebroids and groupoids, as well as what are called higher Lie algebras and algebroids, which generalize ordinary Lie algebras and groups and which appear in more recent proposals for new type of gauge theories. This will in particular entail also some super-geometrical tools for their definition. The aim then is to use these methods to look at characteristic classes (of the standard as well as the more general setting), to introduce gauge theories such as the Poisson sigma model or the more general AKSZ sigma models on the side of topological gauge theories, and Curved Yang-Mills Higgs as well as Higher gauge theories on the side of theories with physical degrees of freedom.

Prerequisites: Basic knowledge of differential geometry (manifolds, differential forms, ...). This can be attained through an at least partially index-free course in General Relativity for physics students, or in a standard course on Differential Geometry for a mathematics student. It is also possible to take at least part of an online course for preparation, such as https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic

Art der Leistungskontrolle und erlaubte Hilfsmittel

Two exams (written and/or oral).

Mindestanforderungen und Beurteilungsmaßstab

In total, one needs 50% of all points to pass the course. The first exam counts 30% to the total mark, the second 70%.

Prüfungsstoff

Content of the course

Literatur


Zuordnung im Vorlesungsverzeichnis

Doktorat Physik, M-ERG

Letzte Änderung: Di 03.09.2024 12:27