Ward Identity and Basis Tensor Gauge Theory at One Loop

TL;DR

This paper introduces a reformulation of gauge theory called basis tensor gauge theory (BTGT), establishes Ward identities for its symmetries, and verifies their quantum consistency through one-loop renormalization of scalar QED.

Contribution

It develops the BTGT formalism, identifies its associated Ward identities, and demonstrates their quantum stability via explicit one-loop renormalization.

Findings

BTGT formalism successfully reproduces standard gauge theory results

Ward identities for BTGT and gauge symmetries are derived and verified

Scalar QED is renormalized at one-loop using dimensional regularization within BTGT

Abstract

Basis tensor gauge theory (BTGT) is a reformulation of ordinary gauge theory that is an analog of the vierbein formulation of gravity and is related to the Wilson line formulation. To match ordinary gauge theories coupled to matter, the BTGT formalism requires a continuous symmetry that we call the BTGT symmetry in addition to the ordinary gauge symmetry. After classically interpreting the BTGT symmetry, we construct using the BTGT formalism the Ward identities associated with the BTGT symmetry and the ordinary gauge symmetry. As a way of testing the quantum stability and the consistency of the Ward identities with a known regularization method, we explicitly renormalize the scalar QED at one-loop using dimensional regularization using the BTGT formalism.