A Realist Interpretation of Unitarity in Quantum Gravity

Fuente: arXiv
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Autores principales: Sen, Indrajit, Alexander, Stephon, Dressel, Justin
Formato: Preprint
Publicado: 2023
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author Sen, Indrajit
Alexander, Stephon
Dressel, Justin
author_facet Sen, Indrajit
Alexander, Stephon
Dressel, Justin
contents Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalizability and the problem of time. We take a realist approach based on pilot-wave theory to address this issue in the Ashtekar formulation of the Wheeler-DeWitt equation. We use the postulate of a definite configuration in the theory to define a global time for the gravitational-fermionic system recently discussed in (Phys. Rev. D 106.10 (2022): 106012), by parameterizing a variation of a Weyl-spinor that depends on the Kodama state. The total Hamiltonian constraint yields a time-dependent Schrodinger equation, without semi-classical approximations, which we use to derive a local continuity equation over the configuration space. We implement the reality conditions at the level of the guidance equation, and obtain a real spin-connection, extrinsic curvature and triad along the system trajectory. We obtain quantum corrections to deSitter spacetime from the guidance equation. The non-normalizable Kodama state is naturally factored out of the full quantum state in the conserved current density, opening the possibility for quantum-mechanical unitarity. We also give a pilot-wave generalisation of the notion of unitarity applicable to non-normalizable states, and show the existence of equilibrium density for our system. Lastly, we find unitary states in mini-superspace by finding an approximate solution to the Hamiltonian constraint.
format Preprint
id arxiv_https___arxiv_org_abs_2310_15157
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle A Realist Interpretation of Unitarity in Quantum Gravity
Sen, Indrajit
Alexander, Stephon
Dressel, Justin
General Relativity and Quantum Cosmology
Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
Quantum Physics
Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalizability and the problem of time. We take a realist approach based on pilot-wave theory to address this issue in the Ashtekar formulation of the Wheeler-DeWitt equation. We use the postulate of a definite configuration in the theory to define a global time for the gravitational-fermionic system recently discussed in (Phys. Rev. D 106.10 (2022): 106012), by parameterizing a variation of a Weyl-spinor that depends on the Kodama state. The total Hamiltonian constraint yields a time-dependent Schrodinger equation, without semi-classical approximations, which we use to derive a local continuity equation over the configuration space. We implement the reality conditions at the level of the guidance equation, and obtain a real spin-connection, extrinsic curvature and triad along the system trajectory. We obtain quantum corrections to deSitter spacetime from the guidance equation. The non-normalizable Kodama state is naturally factored out of the full quantum state in the conserved current density, opening the possibility for quantum-mechanical unitarity. We also give a pilot-wave generalisation of the notion of unitarity applicable to non-normalizable states, and show the existence of equilibrium density for our system. Lastly, we find unitary states in mini-superspace by finding an approximate solution to the Hamiltonian constraint.
title A Realist Interpretation of Unitarity in Quantum Gravity
topic General Relativity and Quantum Cosmology
Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
Quantum Physics
url https://arxiv.org/abs/2310.15157