Functional integration on spaces of connections
Jul, 1995Citations per year
Abstract:
Let be a compact connected Lie group and a smooth principal -bundle. Let a `cylinder function' on the space \A of smooth connections on be a continuous function of the holonomies of along finitely many piecewise smoothly immersed curves in , and let a generalized measure on \A be a bounded linear functional on cylinder functions. We construct a generalized measure on the space of connections that extends the uniform measure of Ashtekar, Lewandowski and Baez to the smooth case, and prove it is invariant under all automorphisms of , not necessarily the identity on the base space . Using `spin networks' we construct explicit functions spanning the corresponding Hilbert space L~2(\A/\G), where \G is the group of gauge transformations.References(12)
Figures(0)