Group Field Theory: An overview

TL;DR

This paper provides an overview of group field theory, a higher-dimensional extension of matrix models, highlighting its role in quantum gravity and its potential for defining a physical scalar product and third quantization.

Contribution

It introduces group field theory as a promising framework for background-independent quantum gravity, connecting it to third quantization and scalar product formulation.

Findings

Proposes group field theory as a natural extension of matrix models.

Shows how the theory offers a candidate for the physical scalar product.

Explains the third quantization perspective in quantum gravity.

Abstract

We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that this theory leads to a natural proposal for the physical scalar product of quantum gravity. We also show in which sense this theory provides a third quantization point of view on quantum gravity.