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arXiv · hep-th/9907042

Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections

M. Bojowald·H. A. Kastrup
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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.

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M. Bojowald, H. A. Kastrup. 1999-07-07. Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections. https://doi.org/10.1088/0264-9381%2F17%2F15%2F311

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