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  Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity

Tomlin, C., & Varadarajan, M. (2013). Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity. Physical Review D, 87: 044039. doi:10.1103/PhysRevD.87.044039.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-EE95-E Version Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-EE96-C
Genre: Journal Article

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 Creators:
Tomlin, Casey1, Author
Varadarajan, Madhavan, Author
Affiliations:
1Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_67201              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
 Abstract: The G -->0 limit of Euclidean gravity introduced by Smolin is described by a generally covariant U(1)xU(1)xU(1) gauge theory. The Poisson bracket algebra of its Hamiltonian and diffeomorphism constraints is isomorphic to that of gravity. Motivated by recent results in Parameterized Field Theory and by the search for an anomaly-free quantum dynamics for Loop Quantum Gravity (LQG), the quantum Hamiltonian constraint of density weight 4/3 for this U(1)xU(1)xU(1) theory is constructed so as to produce a non-trivial LQG-type representation of its Poisson brackets through the following steps. First, the constraint at finite triangulation, as well as the commutator between a pair of such constraints, are constructed as operators on the `charge' network basis. Next, the continuum limit of the commutator is evaluated with respect to an operator topology defined by a certain space of `vertex smooth' distributions. Finally, the operator corresponding to the Poisson bracket between a pair of Hamiltonian constraints is constructed at finite triangulation in such a way as to generate a `generalised' diffeomorphism and its continuum limit is shown to agree with that of the commutator between a pair of finite triangulation Hamiltonian constraints. Our results in conjunction with the recent work of Henderson, Laddha and Tomlin in a 2+1-dimensional context, constitute the necessary first steps toward a satisfactory treatment of the quantum dynamics of this model.

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 Dates: 2012-10-252013
 Publication Status: Published in print
 Pages: 57 pages, 9 figures
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1210.6869
DOI: 10.1103/PhysRevD.87.044039
URI: http://arxiv.org/abs/1210.6869
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : Published for the American Physical Society by the American Institute of Physics
Pages: - Volume / Issue: 87 Sequence Number: 044039 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258