Gravitational null rays are quantized in a diffeomorphism-covariant way using the gravitational dressing time as quantum reference frame, producing a Virasoro crossed-product algebra of gauge-invariant observables.
A Uniqueness Theorem for Constraint Quantization
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This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called ``rigging maps'' associated with Refined Algebraic Quantization, a particular realization of the Dirac scheme. Our main result is to provide a condition under which the rigging map is unique, in which case we also show that it is given by group averaging techniques. Our results comprise all cases where the gauge group is a finite-dimensional Lie group.
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Topology change in canonical JT gravity resolves the firewall paradox by making the connected two-interior branch dominate after Page time, with gravitational constraints annihilating the firewall branch and identifying horizon vacuum and early radiation purity as the same Dirac observable.
Reviews construction of physical inner products in canonical quantum gravity via group averaging and BRST formalism, illustrated in mini-superspace models and connected to path integrals.
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