On the renormalisability of gauge invariant extensions of the squared gauge potential

TL;DR

This paper investigates the renormalisability of gauge invariant extensions of the squared gauge potential, concluding they are non-local and only renormalisable within specific gauges, challenging recent claims about ghost fields' roles.

Contribution

It demonstrates that gauge invariant extensions of the squared gauge potential are non-local and cannot be universally renormalised, refuting the idea that ghost fields are essential for such extensions.

Findings

Extensions have long-range non-localities.

Renormalisation depends on specific gauges.

Ghost fields are not indispensable for non-local extensions.

Abstract

We show that gauge invariant extensions of the local functional $\cO = \frac12\int d^4x A^2$ have long range non localities which can only be ``renormalised'' with reference to a specific gauge. Consequently, there is no gauge independent way of claiming the perturbative renormalisability of these extensions. In particular, they are not renormalisable in the modern sense of Weinberg and Gomis. Critically, our study does not support the view that ghost fields play an indispensable role in the extension of a local operator into a non-local one as claimed recently in the literature.