Continuum spin foam model for 3d gravity
Abstract
An example illustrating a continuum spin foam framework is presented. This covariant framework induces the kinematics of canonical loop quantization, and its dynamics is generated by a {\em renormalized} sum over colored polyhedra. Physically the example corresponds to 3d gravity with cosmological constant. Starting from a kinematical structure that accommodates local degrees of freedom and does not involve the choice of any background structure (e. g. triangulation), the dynamics reduces the field theory to have only global degrees of freedom. The result is {\em projectively} equivalent to the TuraevViro model.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 November 2002
 DOI:
 10.1063/1.1509850
 arXiv:
 arXiv:grqc/0205037
 Bibcode:
 2002JMP....43.5612Z
 Keywords:

 04.60.Nc;
 11.10.Cd;
 11.15.Ha;
 02.40.Re;
 Lattice and discrete methods;
 Axiomatic approach;
 Lattice gauge theory;
 Algebraic topology;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 12 pages, 3 figures