A simple strategy for renormalization: QED at one-loop level

TL;DR

This paper presents a straightforward renormalization strategy for QED at one-loop level that avoids artificial regularization, using effective field theory principles and Ward identities to manage ambiguities.

Contribution

It introduces a simple, regularization-free renormalization method for QED based on effective field theory and Ward identities, with a technical theorem on momentum routing.

Findings

No infinities or ambiguities arise in the method.

Ward identities reduce the number of ambiguities.

Renormalization group equations are derived as decoupling theorems.

Abstract

We demonstrate our simple strategy for renormalization with QED at one-loop level, basing on an elaboration of the effective field theory philosophy. No artificial regularization or deformation of the original theory is introduced here and hence no manipulation of infinities, ambiguities arise instead of infinities. Ward identities first come to reduce the number of ambiguities, the residual ones could in principle be removed by imposing physical boundary conditions. Renormalization group equations arise as "decoupling theorems" in the underlying theory perspective. In addition, a technical theorem concerning routing of external momenta is also presented and illustrated with the self-energy and vertex function as examples.