Spin foam quantization and anomalies
Abstract
The most common spin foam models of gravity are widely believed to be discrete path integral quantizations of the Plebanski action. However, their derivation in present formulations is incomplete and lower dimensional simplex amplitudes are left open to choice. Since their largespin behavior determines the convergence properties of the statesum, this gap has to be closed before any reliable conclusion about finiteness can be reached. It is shown that these amplitudes are directly related to the path integral measure and can in principle be derived from it, requiring detailed knowledge of the constraint algebra and gauge fixing. In a related manner, minimal requirements of background independence provide non trivial restrictions on the form of an anomaly free measure. Many models in the literature do not satisfy these requirements. A simple model satisfying the above consistency requirements is presented which can be thought of as a spin foam quantization of the HusainKuchař model.
 Publication:

General Relativity and Gravitation
 Pub Date:
 April 2010
 DOI:
 10.1007/s1071400908929
 arXiv:
 arXiv:grqc/0303026
 Bibcode:
 2010GReGr..42..877B
 Keywords:

 Spin foam models;
 Loop quantum gravity;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 32 pages