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

1996/06/29 by T. Thiemann · 21 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantum gravity #Euclidean geometry #Euclidean quantum gravity #Hamiltonian (control theory) #Hamiltonian constraint #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Operator (biology) #Quantum Electrodynamics and Casimir Effect #Quantum gravity #Renormalization #Spin foam #gr-qc #hep-th

paper · pdf · doi:10.1016/0370-2693(96)00532-1

published as Phys.Lett. B380 (1996) 257-264 · 10 pages, Latex, to appear in Physics Letters B (in press)

arxiv created 1996/06/29 · openalex publication_date 1996/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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 Poincaré group including the quantum ADM energy.

Citations

• New Variables for Classical and Quantum Gravity
• New Hamiltonian formulation of general relativity

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