Algebraic approach to the frozen formalism problem of time

The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic reduction that avoids difficult requirements such as the computation of a complete set of Dirac observables or the construction of a physical Hilbert space. In addition, the new algebraic treatment makes it possible to implement a consistent realization of the gauge structure off the constraint surface. As a consequence, previously unrecognized consistency conditions are imposed on deparametrization - the method traditionally used to unfreeze evolution in completely constrained systems. A detailed discussion of how the new formulation extends previous semiclassical results shows that an internal time degree of freedom need not be semiclassical in order to define a consistent quantum evolution.

© American Physical Society (APS) [Algebraic approach to the frozen formalism problem of time. Physical Review D 107, 2 (2023)]

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Work Title Algebraic approach to the frozen formalism problem of time
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Open Access
Creators
  1. Martin Bojowald
  2. Artur Tsobanjan
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Physical Review D
Publication Date January 3, 2023
Publisher Identifier (DOI)
  1. https://doi.org/10.1103/PhysRevD.107.024003
Deposited April 05, 2024

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  • Updated Publisher, Publisher Identifier (DOI), Description, and 2 more Show Changes
    Publisher
    • Physical Review D
    Publisher Identifier (DOI)
    • https://doi.org/10.1103/PhysRevD.107.024003
    Description
    • The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic reduction that avoids difficult requirements such as the computation of a complete set of Dirac observables or the construction of a physical Hilbert space. In addition, the new algebraic treatment makes it possible to implement a consistent realization of the gauge structure off the constraint surface. As a consequence, previously unrecognized consistency conditions are imposed on deparametrization - the method traditionally used to unfreeze evolution in completely constrained systems. A detailed discussion of how the new formulation extends previous semiclassical results shows that an internal time degree of freedom need not be semiclassical in order to define a consistent quantum evolution.
    Publication Date
    • 2023-01-03
    Publisher's Statement
    • © American Physical Society (APS) [Algebraic approach to the frozen formalism problem of time. Physical Review D 107, 2 (2023)]
  • Added Creator Martin Bojowald
  • Added Creator Artur Tsobanjan
  • Added AlgebraicPoTPRD-1.pdf
  • Updated License Show Changes
    License
    • https://rightsstatements.org/page/InC/1.0/
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