An operator-algebraic quantization of the characteristic initial-value problem yields a candidate on-shell algebra for a gravitational subregion bounded by two null hypersurfaces.
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Canonical Quantum Gravity and the Problem of Time
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abstract
This is the write-up of my lectures at the NATO Summer School held in Salamanca in June 1992. The paper deals with the problem of time in quantum gravity. All the major schemes are reviewed. Please note that the paper is in two parts for ease of email transmission; this is part 1. The mailer from gr-qc may further subdivide these two sections.
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Extends quantum reference frames to quantum reference fields in linearized quantum gravity and derives unitary maps implementing relational gauge-invariant observables between quantum perspectives.
Optimal transport yields a generalized Wasserstein distance on field space, obtained from a WKB expansion of a Schrödinger equation and extended to dynamical gravity via the Wheeler-DeWitt equation in the ADM formalism.
Extends classical Lie theory with Lie's Algorithm and a commuting pentagon invariance criterion to locally resolve the Problem of Time via background independence.
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
In diffeomorphism-invariant models, invariant content requires spatiotemporal structures beyond correlations, as correlations are invariant only in a generalized non-smooth sense and spatiotemporal relations are also invariant.
Constructs a phase space for gravitational degrees of freedom on null ray segments with commuting localized observables via edge modes and dressing time, then introduces an effective classical theory with Virasoro deformations to capture diffeomorphism anomalies and distinguish gauge, physical, and
Proposes reducing quantum gravity dynamics to Regge-Teitelboim boundary charges in an asymptotic proper-time gauge, yielding a Berry-phase effective Hamiltonian after integrating out bulk modes.
In a quantum Bianchi type-I cosmology, the conditional probability density for zero volume vanishes for all clock times, resolving the classical singularity via Page-Wootters relational dynamics.
Postquantum classical gravity requires stochastic spacetime fluctuations consisting of a diffusing spin-2 field and spin-0 scalar whose noise is constrained by LISA Pathfinder and decoherence bounds.
Relational quantization of the Schwarzschild black hole interior resolves the singularity with a quantum bounce, finite Kretschmann scalar, bounded area, and black-hole-to-white-hole transition.
citing papers explorer
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Quantization of Gravity on Null Hypersurfaces
An operator-algebraic quantization of the characteristic initial-value problem yields a candidate on-shell algebra for a gravitational subregion bounded by two null hypersurfaces.
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Quantum Reference Fields Transformations in Linearized Quantum Gravity
Extends quantum reference frames to quantum reference fields in linearized quantum gravity and derives unitary maps implementing relational gauge-invariant observables between quantum perspectives.
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Optimal paths across potentials on scalar field space
Optimal transport yields a generalized Wasserstein distance on field space, obtained from a WKB expansion of a Schrödinger equation and extended to dynamical gravity via the Wheeler-DeWitt equation in the ADM formalism.
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Problem of Time and Background Independence: classical version's higher Lie Theory
Extends classical Lie theory with Lie's Algorithm and a commuting pentagon invariance criterion to locally resolve the Problem of Time via background independence.
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Wormholes as red herrings: reflection positivity and the reconstruction of unitary quantum field theories
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
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Diffeomorphism-Invariant Quantities in Phase Space: More than Correlations
In diffeomorphism-invariant models, invariant content requires spatiotemporal structures beyond correlations, as correlations are invariant only in a generalized non-smooth sense and spatiotemporal relations are also invariant.
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Localization and anomalous reference frames in gravity
Constructs a phase space for gravitational degrees of freedom on null ray segments with commuting localized observables via edge modes and dressing time, then introduces an effective classical theory with Virasoro deformations to capture diffeomorphism anomalies and distinguish gauge, physical, and
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Quantum Gravity Beyond the Bulk
Proposes reducing quantum gravity dynamics to Regge-Teitelboim boundary charges in an asymptotic proper-time gauge, yielding a Berry-phase effective Hamiltonian after integrating out bulk modes.
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Singularity Resolution in Quantum Cosmology via Page-Wootters Formalism
In a quantum Bianchi type-I cosmology, the conditional probability density for zero volume vanishes for all clock times, resolving the classical singularity via Page-Wootters relational dynamics.
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Stochastic modes in postquantum classical gravity
Postquantum classical gravity requires stochastic spacetime fluctuations consisting of a diffusing spin-2 field and spin-0 scalar whose noise is constrained by LISA Pathfinder and decoherence bounds.
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Relational quantum dynamics of the black hole interior: singularity resolution and quantum bounce
Relational quantization of the Schwarzschild black hole interior resolves the singularity with a quantum bounce, finite Kretschmann scalar, bounded area, and black-hole-to-white-hole transition.