Generalised group field theories and quantum gravity transition amplitudes

TL;DR

This paper introduces a generalized group field theory framework incorporating proper time and mass variables, enabling derivation of various quantum gravity transition amplitudes, including causal and a-causal models, from a unified formalism.

Contribution

It extends group field theories to include proper time and mass variables, unifying causal and a-causal quantum gravity transition amplitudes within a single formalism.

Findings

Derivation of causal spin foam models from the generalized formalism

Connection between causal transition amplitudes and simplicial gravity actions

Unified framework for different quantum gravity transition amplitudes

Abstract

We construct a generalised formalism for group field theories, in which the domain of the field is extended to include additional proper time variables, as well as their conjugate mass variables. This formalism allows for different types of quantum gravity transition amplitudes in perturbative expansion, and we show how both causal spin foam models and the usual a-causal ones can be derived from it, within a sum over triangulations of all topologies. We also highlight the relation of the so-derived causal transition amplitudes with simplicial gravity actions.