Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
نویسنده
چکیده
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 AshtekarLewandowski 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 quantum electromagnetism and spherically symmetric quantum gravity. e-mail address: [email protected] e-mail address: [email protected]
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