Master constraint approach to quantum-reduced loop gravity

Abstract

We introduce a master constraint operator on the kinematical Hilbert space of loop quantum gravity representing a set of gauge conditions which classically fix the densitized triad to be diagonal. We argue that the master constraint approach provides a natural and systematic way of carrying out the quantum gauge-fixing procedure which underlies the model known as quantum-reduced loop gravity. The Hilbert space of quantum-reduced loop gravity is obtained as a particular space of solutions of the gauge-fixing master constraint operator. We give a concise summary of the fundamental structure of the quantum-reduced framework, and consider several possible extensions thereof, for which the master constraint formulation provides a convenient starting point. In particular, we propose a generalization of the standard Hilbert space of quantum-reduced loop gravity, which may be relevant in the application of the quantum-reduced model to physical situations in which the Ashtekar connection is not diagonal.

v2: 29+1 pages, 2 figures. A couple of minor corrections and clarifications. Expanded discussion to provide more details, particularly in section 5. Version accepted for publication in Classical and Quantum Gravity. v1: 26+1 pages, 2 figures

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Cited by in corpus (1)

• On the dynamics of single-vertex states in quantum-reduced loop gravity