Diffeomorphism-Invariant Spin Network States
| dc.creator | Baez, John C. | |
| dc.creator | Sawin, Stephen | |
| dc.date | 1997-08-04 | |
| dc.date | 1997-08-08 | |
| dc.date.accessioned | 2026-07-07T09:08:50Z | |
| dc.date.available | 2026-07-07T09:08:50Z | |
| dc.description | We extend the theory of diffeomorphism-invariant spin network states from the real-analytic category to the smooth category. Suppose that G is a compact connected semisimple Lie group and P -> M is a smooth principal G-bundle. A `cylinder function' on the space of smooth connections on P is a continuous complex function of the holonomies along finitely many piecewise smoothly immersed curves in M. We construct diffeomorphism-invariant functionals on the space of cylinder functions from `spin networks': graphs in M with edges labeled by representations of G and vertices labeled by intertwining operators. Using the `group averaging' technique of Ashtekar, Marolf, Mourao and Thiemann, we equip the space spanned by these `diffeomorphism-invariant spin network states' with a natural inner product. | |
| dc.description | 13 pages, LaTeX, one encapsulated Postscript figure, some corrections in the definition of the inner product | |
| dc.identifier | https://arxiv.org/abs/q-alg/9708005 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9708005 | |
| dc.identifier | Jour. Funct. Analysis, 158 (1998) 253-266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150864 | |
| dc.subject | Quantum Algebra | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Diffeomorphism-Invariant Spin Network States | |
| dc.type | text |