Quantum Cauchy surfaces in canonical quantum gravity. (29th August 2016)

• Record Type: Journal Article
• Authors: Lin, Chun-Yen
• Is Part Of: Classical and quantum gravity. Volume 33:Number 18(2016:Sep.)
• Publication Date: 2016-08-29
• Subjects: canonical quantum gravity -- refined algebraic quantization -- Dirac observables -- Schrödinger picture; Quantum gravity -- Periodicals; Gravitation -- Periodicals; Relativity (Physics) -- Periodicals; Space and time -- Periodicals; Periodicals; 521.1
• DOI: 10.1088/0264-9381/33/18/185009
• Languages: English
• ISSNs: 0264-9381

Abstract

Abstract: For a Dirac theory of quantum gravity obtained from the refined algebraic quantization procedure, we propose a quantum notion of Cauchy surfaces. In such a theory, there is a kernel projector for the quantized scalar and momentum constraints, which maps the kinematic Hilbert space K into the physical Hilbert space H . Under this projection, a quantum Cauchy surface isomorphically represents a physical subspace D ⊂ H with a kinematic subspace V ⊂ K . The isomorphism induces the complete sets of Dirac observables in D, which faithfully represent the corresponding complete sets of self-adjoint operators in V . Due to the constraints, a specific subset of the observables would be 'frozen' as number operators, providing a background physical time for the rest of the observables. Therefore, a proper foliation with the quantum Cauchy surfaces may provide an observer frame describing the physical states of spacetimes in a Schrödinger picture, with the evolutions under a specific physical background. A simple model will be supplied as an initiative trial.