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A combinatorial and field theoretic path to quantum gravity: the new challenges of group field theory. (English) Zbl 1223.83025
Ebrahimi-Fard, Kurusch (ed.) et al., Combinatorics and physics. Mini-workshop on renormalization, December 15–16, 2006, conference on combinatorics and physics, March 19–23, 2007, Bonn, Germany. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-5329-0/pbk). Contemporary Mathematics 539, 325-347 (2011).
Summary: Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link between different approaches such as loop quantum gravity and simplicial quantum gravity. After a brief introduction to the GFT formalism we put forward a long but still far from exhaustive list of open issues that this line of research faces, and that could be represent interesting challenges for mathematicians and mathematical physicists alike.
For the entire collection see [Zbl 1214.81008].

83C47 Methods of quantum field theory in general relativity and gravitational theory
83C45 Quantization of the gravitational field
81V17 Gravitational interaction in quantum theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
81T20 Quantum field theory on curved space or space-time backgrounds
81S40 Path integrals in quantum mechanics