08.10.2024, 10:15 - 11:45
– 3.06.H02
Kálmán Lecture
Particle Methods in Machine Learning and Inverse Problems
Martin Burger, Helmholtz Imaging
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.