Regularization in quantum field theory from the causal point of view

TL;DR

This paper reviews the causal approach to perturbative quantum field theory, emphasizing its mathematical rigor and extension to higher spin theories, including gravity, contrasting it with other regularization methods.

Contribution

It extends the causal perturbation theory framework to higher spin fields and gravity, providing detailed examples and technical comparisons with other regularization techniques.

Findings

Causal perturbation theory offers a rigorous basis for renormalization.

The method is extended to include theories with higher spin and gravity.

Differences between causal approach and dimensional regularization are highlighted.

Abstract

The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.