Infinite-dimensional Lie Theory for Gauge Groups


Gauge groups occur in mathematical physics as infinite-dimensional symmetry groups of gauge theories. These theories are formulated in terms of a smooth K-principal bundle q:P→ M, and the gauge group may be identified with the space of smooth K-invariant mappings C(P,K)K. If the bundle is trivial or K is abelian, then C(P,K)K is isomorphic to C(M,K), but in general (e.g. for so called Yang-Mills Theories) this is not always the case.
This talk describes how Lie theoretic results for C(M,K) can be transfered to C(P,K)K. This will cover central extensions of C(P,K)K, actions of Aut(P) and the calculation of πn(C(P,K)K) for bundles over compact orientable surfaces M.
christoph AT