Classical Group Field Theory

TL;DR

This paper applies classical field theory formalism to group field theories, analyzing symmetries and conserved quantities like energy-momentum and dilatation currents in local and nonlocal models.

Contribution

It extends classical field theory methods to group field theories, deriving conserved currents and exploring symmetry properties in both local and nonlocal contexts.

Findings

Derived energy-momentum tensor for group field theories

Identified dilatation current and its properties

Analyzed translation and dilatation symmetries in various models

Abstract

The ordinary formalism for classical field theory is applied to dynamical group field theories. Focusing first on a local group field theory over one copy of SU(2) and, then, on more involved nonlocal theories (colored and non colored) defined over a tensor product of the same group, we address the issue of translation and dilatation symmetries and the corresponding Noether theorem. The energy momentum tensor and dilatation current are derived and their properties identified for each case.