
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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License | In Copyright (Rights Reserved) |
Work Type | Article |
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Publication Date | January 3, 2023 |
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Deposited | April 05, 2024 |
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