Finite Callan-Symanzik renormalisation for multiple scalar fields

TL;DR

This paper extends a divergence-free renormalisation method based on Callan-Symanzik equations to multiple scalar fields, providing a finite approach applicable to complex quantum field theories.

Contribution

It generalizes a historic finite renormalisation technique to systems with multiple interacting scalar fields, broadening its applicability.

Findings

The method is finite and divergence-free.

It is generalized from single to multiple scalar fields.

Applicable to arbitrary numbers of interacting fields.

Abstract

We study a finite, divergence free approach to renormalisation originally proposed in the early '70s by Blaer and Young, and Callan. It is based on equations similar to the Callan-Symanzik equations, and introduced in the context of $\lambda \phi^4$ theory. We generalise this method to the case of two interacting scalar fields, with obvious generalisation to an arbitrary number of fields.