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Group Averaging and Refined Algebraic Quantization: Where are we now?

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arxiv gr-qc/0011112 v1 pith:FHB2VFA4 submitted 2000-11-30 gr-qc

Donald Marolf This is my paper · ORCID
classification gr-qc
keywords algebraicaveraginggroupquantizationrefinedalgorithmsconstrainedconstructive
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Refined Algebraic Quantization and Group Averaging are powerful methods for quantizing constrained systems. They give constructive algorithms for generating observables and the physical inner product. This work outlines the current status of these ideas with an eye toward quantum gravity. The main goal is provide a description of outstanding problems and possible research topics in the field.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Chaos and the Emergence of the Cosmological Horizon

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    Finite-mass observers in dS2 have non-commuting type I algebras, and their OTOC shows a Lyapunov exponent 4π/β_dS, twice the de Sitter bound.

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    Semiclassical pure AdS3 gravity states, labelled by fixed-area geodesic networks, are mapped to CFT2 primary states whose wavefunctions are networks of OPE coefficients.

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    For ideal quantum reference frames with a single constraint, the perspective-neutral, algebraic, and effective semiclassical approaches describe the same physics and the same frame-switching rules.

  4. Observers and Timekeepers: From the Page-Wootters Mechanism to the Gravitational Path Integral

    hep-th 2025-06 conditional novelty 6.0 of 10

    Metric summation produces the problem of time, topology summation produces the one-dimensional Hilbert space, and a timekeeper path integral gives observer-dependent holography.

  5. Nonperturbative Quantum Gravity in a Closed Lorentzian Universe

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    In a closed universe with a one-dimensional Hilbert space per alpha-microstate, tracing out unobserved environmental degrees of freedom yields robust, einselected probabilities with errors exponentially suppressed by ...

  6. Crossed products and quantum reference frames: on the observer-dependence of gravitational entropy

    hep-th 2024-12 accept novelty 6.0 of 10

    Gravitational subregion entropy is observer-dependent: different quantum clocks produce different von Neumann algebras and different entropy functionals for the same global state.

  7. Gravitational Hilbert spaces: invariant and co-invariant states, inner products, gauge-fixing, and BRST

    hep-th 2025-09 unverdicted novelty 4.0 of 10

    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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