/sci/ - Science & Math

>>9602651
Depends on the gauge group [math]G[/math] as well as the manifold [math]M[/math] (obviously). In general the local tangent space [math]T_\alpha \mathcal{A}[/math] can always be constructed, but the difficulty comes when you try to patch together the locally-defined measures, and this requires compactification of the moduli space (unless you don't care about convergence).
The main point is that if your homotopy quotient [math]M \times_G G[/math] is nice enough (i.e. vanishing odd-degree cohomology or a stabilizing Leray spectral sequence), then you the path integration becomes just the equivariant fibre integration, and the stationary phase approximation works via Deligne-Verne. In some cases if the Thom class is trivial you can even identify the path integral with the Euler characterisitc.