Einstein-Cartan Theory and Gauge Symmetry

TL;DR

This paper discusses the non gauge invariant coupling between torsion and gauge fields in Einstein-Cartan theory, emphasizing the importance of gauge invariance for observable quantities.

Contribution

It demonstrates that non gauge invariant couplings can be reconciled with gauge invariance through normal frames and approximations, clarifying their physical relevance.

Findings

Non gauge invariant couplings are significant in Einstein-Cartan theory.

Gauge invariance can be restored using normal frames and delta-function approximations.

Observable quantities remain gauge invariant despite non gauge invariant couplings.

Abstract

We argue that the non gauge invariant coupling between torsion and the Maxwell or Yang-Mills fields in Einstein-Cartan theory can not be ignored. Arguments based in the existence of normal frames in neighbourhoods, and an approximation to a \delta-function, lead to gauge invariant observables.