One Loop Vacuum Polarization without Infinities

TL;DR

The paper introduces a novel technique for calculating one-loop vacuum polarization that avoids infinities and renormalization by eliminating the need for delta functions in Green's functions.

Contribution

It presents a new method that circumvents infinities in quantum field calculations without requiring traditional renormalization procedures.

Findings

Method produces the same results as dimensional renormalization.

No infinities or delta functions are involved in the calculations.

Simplifies vacuum polarization computations.

Abstract

A technique for avoiding infinite integrals in the calculation of the one-loop diagram contribution to the vacuum polarization component of an atomic energy level is presented. This makes renormalization unnecessary. Infinite integrals do not occur because, as it is shown, no delta functions are required for the Green's functions. Thus there are none to overlap. This procedure is shown to produce the same formula as the one obtained by dimensional renormalization.