Scale Invariance in the Causal Approach to Renormalization Theory

TL;DR

This paper investigates scale invariance within the Epstein-Glaser renormalization framework, deriving analogues of Callan-Symanzik equations and revealing how massless fields lead to logarithmic anomalous terms through cohomological analysis.

Contribution

It introduces analogues of Callan-Symanzik equations in Epstein-Glaser renormalization and shows how massless fields produce logarithmic anomalies via cohomology.

Findings

Derived analogues of Callan-Symanzik equations for scalar and Yang-Mills theories.

Identified conditions under which logarithmic anomalous terms arise.

Showed that massless fields lead to cohomologically determined anomalies.

Abstract

The dilation invariance is studied in the framework of Epstein-Glaser approach to renormalization theory. Some analogues of the Callan-Symanzik equations are found and they are applied to the scalar field theory and to Yang-Mills models. We find the interesting result that, if all the fields of the theory have zero masses, then from purely cohomological consideration, one can obtain the anomalous terms of logarithmic type.