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Quantum Symmetry Reduction for Diffeomorphism Invariant Theories of Connections
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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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Emergent field theory
Spacetime geometry and Yang-Mills field strengths are generated from phase-space structure functions, yielding modified gravity and gauge theories with no new degrees of freedom.
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