Inequivalent coherent state representations in group field theory

TL;DR

This paper introduces an algebraic approach to group field theory, exploring non-Fock coherent state representations that break translation symmetry and may better model quantum gravitational phases.

Contribution

It presents a novel algebraic formulation and constructs infinite degrees of freedom representations that could describe effective geometrical phases in quantum gravity.

Findings

Constructed non-Fock coherent state representations with infinite degrees of freedom.

Showed these representations break translation symmetry.

Suggested these models are suitable for describing quantum gravitational phases.

Abstract

In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with infinite number of degrees of freedom on compact base manifolds. We also show that these representations break translation symmetry. Since such representations can be regarded as quantum gravitational systems with an infinite number of fundamental pre-geometric building blocks, they may be more suitable for the description of effective geometrical phases of the theory.