On the relation between reduced quantisation and quantum reduction for spherical symmetry in loop quantum gravity

Abstract

Building on a recent proposal for a quantum reduction to spherical symmetry from full loop quantum gravity, we investigate the relation between a quantisation of spherically symmetric general relativity and a reduction at the quantum level. To this end, we generalise the previously proposed quantum reduction by dropping the gauge fixing condition on the radial diffeomorphisms, thus allowing to make direct contact between previous work on reduced quantisation. A dictionary between spherically symmetric variables and observables with respect to the reduction constraints in the full theory is discussed, as well as an embedding of reduced quantum states to a sub sector of the quantum symmetry reduced full theory states. On this full theory sub sector, the quantum algebra of the mentioned observables is computed and shown to qualitatively reproduce the quantum algebra of the reduced variables in the large quantum number limit for a specific choice of regularisation. Insufficiencies in recovering the reduced algebra quantitatively from the full theory are attributed to the oversimplified full theory quantum states we use.

35 pages; v2: journal version, minor clarifications

References in corpus (10)

• Quantum Nature of the Big Bang: Improved dynamics
• LQG vertex with finite Immirzi parameter
• Black hole evaporation: A paradigm
• Gravity quantized
• Fast Radio Bursts and White Hole Signals
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• A quantum reduction to Bianchi I models in loop quantum gravity
• A symmetric scalar constraint for loop quantum gravity
• General relativity in the radial gauge: Reduced phase space and canonical structure
• A quantum reduction to spherical symmetry in loop quantum gravity

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