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Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity

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arxiv gr-qc/9606088 v1 pith:ACKFCG7R submitted 1996-06-29 gr-qc hep-th

T. Thiemann This is my paper · ORCID
classification gr-qchep-th
keywords constraintoperatorquantumhamiltonianlorentzianoperatorswheeler-dewittanomaly-free
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A Wheeler-Dewitt quantum constraint operator for four-dimensional, non-perturbative Lorentzian vacuum quantum gravity is defined in the continuum. The regulated Wheeler-DeWitt constraint operator is densely defined, does not require any renormalization and the final operator is anomaly-free and at least symmmetric. The technique introduced here can also be used to produce a couple of other completely well-defined regulated operators including but not exhausting a) the Euclidean Wheeler-DeWitt operator, b)the generator of the Wick rotation transform that maps solutions to the Euclidean Hamiltonian constraint to solutions to the Lorentzian Hamiltonian constraint, c) length operators, d) Hamiltonian operators of the matter sector and e) the generators of the asymptotic Poincar\'e group including the quantum ADM energy.

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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. A matrix free action of the Ashtekar-Lewandowski volume operator of loop quantum gravity

    gr-qc 2026-06 unverdicted novelty 7.0 of 10

    Develops a matrix-free SRQ-based action for the AL volume operator that exactly preserves the kernel and supports large-scale Monte Carlo and spectral estimates without dense matrices.

  2. Non-perturbative, background independent Fock representations for canonical quantum gravity

    gr-qc 2026-06 unverdicted novelty 6.0 of 10

    Existence of separable Fock Hilbert spaces for background-independent non-perturbative quantization of general relativity.

  3. Quantum Cosmological Backreactions II: Purely Homogeneous Quantum Cosmology

    gr-qc 2019-06 unverdicted novelty 6.0 of 10

    Space adiabatic perturbation theory applied to homogeneous oscillator models shows that backreactions add correction terms to effective Hamiltonians neglected in the Born-Oppenheimer approximation.

  4. Non-perturbative, background independent canonical quantum gravity in Fock representations

    gr-qc 2026-06 unverdicted novelty 5.0 of 10

    Existence of background-independent Fock representations for canonical quantum gravity with matter, producing a separable Hilbert space unlike LQG.

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