A Lorentzian signature model for quantum general relativity
Abstract
We give a relativistic spin network model for quantum gravity based on the Lorentz group and its qdeformation, 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 fourdimensional rotation group previously studied in grqc/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.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 August 2000
 DOI:
 10.1088/02649381/17/16/302
 arXiv:
 arXiv:grqc/9904025
 Bibcode:
 2000CQGra..17.3101B
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 22 pages, latex, amsfonts, Xypic. Version 3: improved presentation. Version 2 is a major revision with explicit formulae included for the evaluation of relativistic spin networks and the computation of examples which have finite values