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...
| Main Authors: | , |
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| Format: | Article |
| Published: |
2000
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| Online Access: | https://eprints.nottingham.ac.uk/9/ |
| _version_ | 1848790365844275200 |
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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. |
| first_indexed | 2025-11-14T18:11:28Z |
| format | Article |
| id | nottingham-9 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T18:11:28Z |
| publishDate | 2000 |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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/ |