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arXiv · 2212.13961

An algebraic approach to the "frozen formalism" problem of time

Martin Bojowald·Artur Tsobanjan
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Abstract

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 deparameterization -- 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.

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Martin Bojowald, Artur Tsobanjan. 2022-12-28. An algebraic approach to the "frozen formalism" problem of time. https://doi.org/10.1103/physrevd.107.024003

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