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Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections | | M. Bojowald
; H.A. Kastrup
; | | Date: |
7 Jul 1999 | | Journal: | Class.Quant.Grav. 17 (2000) 3009-3043 | | Subject: | hep-th gr-qc | | Affiliation: | RWTH Aachen, Germany | | Abstract: | Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product derived from the Ashtekar-Lewandowski measure for loop quantum gravity, form a Hilbert space of their own. Restriction to this Hilbert space yields a quantum symmetry reduction procedure in the framework of spin network states the structure of which is analyzed in detail. Three illustrating examples are discussed: Reduction of 3+1 to 2+1 dimensional quantum gravity, spherically symmetric electromagnetism and spherically symmetric gravity. | | Source: | arXiv, hep-th/9907042 | | Services: | Forum | Review | PDF | Favorites | |
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