Functional Integration on Spaces of Connections
| dc.creator | Baez, John C. | |
| dc.creator | Sawin, Stephen | |
| dc.date | 1995-07-20 | |
| dc.date.accessioned | 2026-07-07T09:16:37Z | |
| dc.date.available | 2026-07-07T09:16:37Z | |
| dc.description | Let $G$ be a compact connected Lie group and $P \to M$ a smooth principal $G$-bundle. Let a `cylinder function' on the space $\A$ of smooth connections on $P$ be a continuous function of the holonomies of $A$ along finitely many piecewise smoothly immersed curves in $M$, 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 $P$, not necessarily the identity on the base space $M$. Using `spin networks' we construct explicit functions spanning the corresponding Hilbert space $L^2(\A/\G)$, where $\G$ is the group of gauge transformations. | |
| dc.description | 24 pages, LaTeX with epsfig, 6 ps figures included via uufiles. PS file available at http://web.mit.edu/org/m/mathdept/www/ | |
| dc.identifier | https://arxiv.org/abs/q-alg/9507023 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9507023 | |
| dc.identifier | J. Funct. Anal., 150 (1997), 1-26 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153417 | |
| dc.subject | Quantum Algebra | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Functional Integration on Spaces of Connections | |
| dc.type | text |