A note on regularization and renormalization

TL;DR

This paper explores the mathematical relationship between regularization and renormalization in the context of differential operators, establishing an isomorphism and illustrating differential renormalization as an example of this technique.

Contribution

It introduces a novel isomorphism between quotient bundles and Fourier counterparts, linking regularization and renormalization in differential operator theory.

Findings

Constructed an isomorphism between quotient bundle and Fourier counterpart.

Demonstrated that differential renormalization exemplifies this isomorphism.

Provided a mathematical framework connecting regularization and renormalization techniques.

Abstract

We look at sections of a function bundle over the space of linear differential operators. We find that one can construct an isomorphism between a certain quotient bundle and the fourier counterpart of the original bundle defined by formal integration by parts. We also show that differential renormalization is an example of this technique.