Algebraic approach to the frozen formalism problem of time

Martin Bojowald, Artur Tsobanjan

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number024003
JournalPhysical Review D
Issue number2
StatePublished - Jan 15 2023

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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