2-Gauge transformations: A cabinet of curiosities

30.10.2020, 11:00  –  Online Seminar
Arbeitsgruppenseminar Analysis

Alfonso Garmendia (Uni Potsdam)

Gauge transformations  are present both in Mathematics and Physics where  they play a key role in  field  theory. In mathematical terms, these transformations are special maps on a principal bundle   and   represent changes of coordinates at a  point of the underlying manifold. We can go a little bit further and study changes of coordinates between two different points in the underlying manifold. This is no longer a principal bundle but a groupoid over the manifold, called the gauge groupoid. We call special maps on the gauge groupoid 2-gauge transformations. Every gauge transformation defines, in a natural way, a 2-gauge transformation.
In this talk, I will give an introduction of the facts listed above and will also show how  these structures are encoded on a strict Lie 2-group action on a the pair groupoid of the principal bundle.