Causal Perturbation Theory and Differential Renormalization

TL;DR

This paper links Causal Perturbation Theory's renormalization process with Differential Renormalization, showing their equivalence and illustrating this connection through examples in scalar field theory.

Contribution

It demonstrates that the subtraction method in Causal Perturbation Theory corresponds to Differential Renormalization, unifying these approaches.

Findings

Equivalence of subtraction methods in different renormalization schemes

Application to scalar field theory in flat and curved spacetime

Explicit examples illustrating the theoretical connection

Abstract

In Causal Perturbation Theory the process of renormalization is precisely equivalent to the extension of time ordered distributions to coincident points. This is achieved by a modified Taylor subtraction on the corresponding test functions. I show that the pullback of this operation to the distributions yields expressions known from Differential Renormalization. The subtraction is equivalent to BPHZ subtraction in momentum space. Some examples from Euclidean scalar field theory in flat and curved spacetime will be presented.