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Quantum field theory on a cosmological, quantum space-time

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arxiv 0901.0933 v3 pith:4M67ZPEB submitted 2009-01-07 gr-qc hep-thmath-phmath.MP

Abhay Ashtekar , Wojciech Kaminski , Jerzy Lewandowski This is my paper · ORCID
classification gr-qchep-thmath-phmath.MP
keywords quantumtheoryfieldclassicalflrwgeometriesspace-timespace-times
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In loop quantum cosmology, Friedmann-LeMaitre-Robertson-Walker (FLRW) space-times arise as well-defined approximations to specific \emph{quantum} geometries. We initiate the development of a quantum theory of test scalar fields on these quantum geometries. Emphasis is on the new conceptual ingredients required in the transition from classical space-time backgrounds to quantum space-times. These include a `relational time' a la Leibnitz, the emergence of the Hamiltonian operator of the test field from the quantum constraint equation, and ramifications of the quantum fluctuations of the background geometry on the resulting dynamics. The familiar quantum field theory on classical FLRW models arises as a well-defined reduction of this more fundamental theory.

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Cited by 4 Pith papers

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

  1. Prism Effect in Quantum Gravity

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    Extended Born-Oppenheimer coupling of the EM field to quantum geometry yields chromatic dispersion of light—a prism effect proposed as an all-energy quantum-gravity probe on a quantum FLRW background.

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    gr-qc 2025-09 conditional novelty 5.0 of 10

    In a Bianchi-I universe with polymer quantization of both geometry and a massless scalar, the matter polymer scale shifts the quantum bounce and alters volume and anisotropy evolution.

  4. Polymer cosmology with polymer matter: Effective dynamics

    gr-qc 2025-02 conditional novelty 5.0 of 10

    A polymer-quantized scalar field on a polymer-quantized FLRW background produces a bounce whose location depends on the matter polymer scale, with generic asymmetric evolution across the bounce.

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