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
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.