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A Lorentzian Signature Model for Quantum General Relativity

Barrett, John W.; Crane, Louis

Authors

JOHN BARRETT john.barrett@nottingham.ac.uk
Professor of Mathematical Physics

Louis Crane



Abstract

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.

Citation

Barrett, J. W., & Crane, L. (2000). A Lorentzian Signature Model for Quantum General Relativity

Journal Article Type Article
Publication Date Jan 1, 2000
Deposit Date Jul 30, 2001
Publicly Available Date Oct 9, 2007
Journal Class.Quant.Grav.
Peer Reviewed Peer Reviewed
Volume 17
Public URL http://eprints.nottingham.ac.uk/id/eprint/9
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf


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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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