06.06.2023, 15 Uhr
Phenomena in High Dimensions
Pierre Youssef (New York University, Abu Dhabi)
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.