Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections

Details Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections

1999-07-07

arxiv.org/abs/hep-th/9907042v1

Class.Quant.Grav. 17 (2000) 3009-3043

Physics

High Energy Physics

High Energy Physics - Theory

43 pages, Latex

Scientific paper

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.

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