Non-transversality of the gluon polarization tensor in a chromomagnetic background

TL;DR

This paper examines the non-transversality of the gluon polarization tensor in a chromomagnetic background, extending previous one-loop results by including arbitrary gauge fixing parameters and deriving related identities.

Contribution

It generalizes the understanding of gluon polarization tensor non-transversality by incorporating arbitrary gauge fixing parameters and deriving associated Slavnov-Taylor identities.

Findings

Confirmed non-transversality in a chromomagnetic background

Derived gauge parameter dependence of the polarization tensor

Extended previous results to arbitrary gauge fixing

Abstract

We investigate the question about the transversality of the gluon polarization tensor in a homogeneous chromomagnetic background field. We re-derive the non transversality known from a pure one loop calculation using the Slavnov-Taylor identities. In addition we generalize the procedure to arbitrary gauge fixing parameter $\xi$ and calculate the $\xi$-dependent part of the polarization tensor.