The group field theory approach to quantum gravity
Abstract
We give a very concise review of the group field theory formalism for nonperturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd quantization of the gravitational field, equivalently of a quantum field theory of simplicial geometry, in which also the topology of space is fully dynamical. We highlight the basic structure of the formalism, and discuss briefly various models that are being studied, some recent results and the many open issues that future research should face. Finally, we point out the connections with other approaches to quantum gravity, such as loop quantum gravity, quantum Regge calculus and dynamical triangulations, and causal sets.
 Publication:

arXiv eprints
 Pub Date:
 July 2006
 DOI:
 10.48550/arXiv.grqc/0607032
 arXiv:
 arXiv:grqc/0607032
 Bibcode:
 2006gr.qc.....7032O
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 17 pages, 2 figures