This lecture focusses on the classical aspects of gauge theories, meant both as an introduction and supplement to quantum field theory courses. Using the gauge principle in classical electrodynamics as starting point and motivation, we will first discuss the basic aspects of classical field theory. After an introduction to Lie-groups and their representations, non-abelian gauge theories will be discussed in detail, focussing on the construction of gauge invariant Lagrangians. We proceed to analyse the spontaneous breaking of symmetries, both in the context of global symmetries (Goldstone theorem) and gauge symmetries (Higgs mechanism). Finally we will discuss non-linear aspects of gauge theories (topological solitons, monopoles) and the associated mathematical concepts (homotopy theory).

The lecture will closely follow the 2002 textbook by Valery Rubakov “Classical theory of gauge fields”

Lecture: Mondays, 9:45 - 11:15, 30.22 Physik-Hörsaal Nr. 4 (Kl. HS B) (first lecture: April 25, 2022)
ILIAS: Organizational details can be found on ILIAS.

In case of questions feel free to contact Robert Ziegler.