Foundational Issues in Group Field Theory

TL;DR

This paper critically examines the foundational issues of group field theory (GFT) in quantum gravity, questioning its interpretative clarity and its connection to covariant and canonical formulations, highlighting unresolved conceptual problems.

Contribution

The paper provides a critical analysis of GFT's foundations, contrasting covariant and canonical approaches, and discusses conceptual and interpretative challenges in quantum gravity.

Findings

GFT may be limited to a computational tool without foundational insight.

Canonical GFT faces issues related to the problem of time.

Serious concerns exist about the justification and interpretation of GFT.

Abstract

In this paper I offer an introduction to group field theory (GFT) and to some of the issues affecting the foundations of this approach to quantum gravity. I first introduce covariant GFT as the theory that one obtains by interpreting the amplitudes of certain spin foam models as Feynman amplitudes in a perturbative expansion. However, I argue that it is unclear that this definition of GFTs amounts to something beyond a computational rule for finding these transition amplitudes and that GFT doesn't seem able to offer any new insight into the foundations of quantum gravity. Then, I move to another formulation of GFT which I call canonical GFT and which uses the standard structures of quantum mechanics. This formulation is of extended use in cosmological applications of GFT, but I argue that it is only heuristically connected with the covariant version and spin foam models. Moreover, I argue that this approach is affected by a version of the problem of time which raises worries about its viability. Therefore, I conclude that there are serious concerns about the justification and interpretation of GFT in either version of it.