Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-11-17
Physics
High Energy Physics
High Energy Physics - Theory
42 pages, 4 figures, notes of lectures presented at the second Modave Summer School on Mathematical Physics, August 2006
Scientific paper
In these lecture notes we will try to give an introduction to the use of the mathematics of fibre bundles in the understanding of some global aspects of gauge theories, such as monopoles and instantons. They are primarily aimed at beginning PhD students. First, we will briefly review the concept of a fibre bundle and define the notion of a connection and its curvature on a principal bundle. Then we will introduce some ideas from topology such as homotopy, topological degree and characteristic classes. Finally, we will apply these notions to the bundle setup corresponding to monopoles and instantons. We will end with some remarks on index theorems and their applications and some hints towards a bigger picture.
Collinucci Andres
Wijns Alexander
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