A Lorentzian Signature Model for Quantum General Relativity

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum mode...

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Main Authors: Barrett, John W., Crane, Louis
Format: Article
Published: 2000
Online Access:https://eprints.nottingham.ac.uk/9/
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author Barrett, John W.
Crane, Louis
author_facet Barrett, John W.
Crane, Louis
author_sort Barrett, John W.
building Nottingham Research Data Repository
collection Online Access
description We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.
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spelling nottingham-92020-05-04T20:32:53Z https://eprints.nottingham.ac.uk/9/ A Lorentzian Signature Model for Quantum General Relativity Barrett, John W. Crane, Louis We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value. 2000 Article PeerReviewed Barrett, John W. and Crane, Louis (2000) A Lorentzian Signature Model for Quantum General Relativity. Class.Quant.Grav., 17 . pp. 3101-3118.
spellingShingle Barrett, John W.
Crane, Louis
A Lorentzian Signature Model for Quantum General Relativity
title A Lorentzian Signature Model for Quantum General Relativity
title_full A Lorentzian Signature Model for Quantum General Relativity
title_fullStr A Lorentzian Signature Model for Quantum General Relativity
title_full_unstemmed A Lorentzian Signature Model for Quantum General Relativity
title_short A Lorentzian Signature Model for Quantum General Relativity
title_sort lorentzian signature model for quantum general relativity
url https://eprints.nottingham.ac.uk/9/