Table of Contents
Journal of Gravity
Volume 2013, Article ID 549824, 28 pages
http://dx.doi.org/10.1155/2013/549824
Review Article

Spin Foam Models with Finite Groups

1DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
2MPI for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, 14476 Potsdam, Germany

Received 30 March 2013; Accepted 3 June 2013

Academic Editor: Kazuharu Bamba

Copyright © 2013 Benjamin Bahr et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.