Infinity in the regularization of Quantum Electrodynamics: A non standard Alternative

TL;DR

This paper explores the use of non-standard analysis to address infinities in Quantum Electrodynamics regularization, aiming to clarify the mathematical foundations and distinguish them from physical renormalization, with the Casimir effect as a case study.

Contribution

It introduces non-standard analysis as a novel approach to regularization in QED, providing a clearer mathematical framework compared to traditional methods.

Findings

Non-standard analysis offers a consistent way to handle infinities in QED.

Distinction between physical renormalization and mathematical regularization is clarified.

Application to the Casimir effect demonstrates the approach's potential.

Abstract

We review the concept of infinity as applied to regularization procedures in Quantum Electrodynamics. A clear distinction that is lacking in current literature is made between the physical contents of renormalization, and the mathematical aspects of regularization. Robinson's non-standard analysis is offered as a means to settle the ambiguities of the theory, in the spirit of Paul Dirac's well known comments concerning the weak status of the mathematics used in traditional regularization schemes. As a case study we consider the Casimir effect