Finite field theories and causality

TL;DR

This paper introduces causal perturbation theory, a rigorous mathematical framework for renormalization in quantum field theory that avoids infinities and has been applied to various gauge theories.

Contribution

It provides a condensed overview of causal perturbation theory, emphasizing its mathematical rigor and its application to scalar and gauge quantum field theories.

Findings

Causal perturbation theory avoids infinities in loop calculations.

It has been successfully applied to scalar and gauge theories.

The approach provides a sound mathematical basis for renormalization.

Abstract

A condensed introduction to the basic concepts of causal perturbation theory is given. 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 by avoiding infinities from the outset. It goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser published in 1973, where a specific causality condition was imposed at every order of perturbation theory in the case of scalar quantum field theory such that divergent integrals could be avoided in actual calculations of loop diagrams. In the meantime, the causal approach has been applied also to a wide range of gauge theories.