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.
Keywords
Cite
@article{arxiv.2311.16648,
title = {Master constraint approach to quantum-reduced loop gravity},
author = {Ilkka Mäkinen},
journal= {arXiv preprint arXiv:2311.16648},
year = {2024}
}
Comments
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