Field redefinition and renormalisability in scalar field theories

TL;DR

This paper investigates how field redefinitions affect the renormalisability of scalar field theories, demonstrating that renormalisability is preserved under such transformations using the background field method, with simplified counter-term calculations in polar coordinates.

Contribution

It shows that renormalisability remains intact under field redefinitions in scalar theories and introduces a simplified approach using polar coordinates for complex scalar fields.

Findings

Renormalisability is preserved after field redefinitions.

Background field expansion is effective for analyzing renormalisability.

Polar coordinates simplify one-loop counter-term calculations.

Abstract

We have addressed the issue of field redefinition in connection with renormalisability. Our study is restricted to theories of interacting scalar fields. We have, in particular, shown that if a theory is renormalisable in the usual power-counting sense then it remains renormalisable in the same sense after a change of variables. This is due to the use of the powerful method of the background field expansion. In the case of a single complex sclar field, it turns out that the determination of the counter-terms is much simpler when polar coordinates are used. We illustate this by carrying out a one-loop calculation in the latter case.