From arbitrariness to ambiguities in the evaluation of perturbative physical amplitudes and their symmetry relations

TL;DR

This paper presents a general calculational approach to divergent perturbative amplitudes in quantum field theory, emphasizing the role of symmetries in resolving ambiguities and providing insights into anomalies.

Contribution

It introduces a symmetry-guided method to handle divergences in perturbative calculations, clarifying the role of regularization and anomalies.

Findings

Symmetry properties help identify necessary choices to avoid ambiguities.

The approach offers a deeper understanding of regularization methods.

Insights into the justification of triangle anomalies in quantum field theory.

Abstract

A very general calculational strategy is applied to the evaluation of the divergent physical amplitudes which are typical of perturbative calculations. With this approach in the final results all the intrinsic arbitrariness of the calculations due to the divergent character is still present. We show that by using the symmetry properties as a guide to search for the (compulsory) choices in such a way as to avoid ambiguities, a deep and clear understanding of the role of regularization methods emerges. Requiring then an universal point of view for the problem, as allowed by our approach, very interesting conclusions can be stated about the possible justifications of most intriguing aspect of the perturbative calculations in quantum field theory: the triangle anomalies.