Modified Coulomb potential with virtual photons following a canonical distribution

TL;DR

This paper proposes a modified Coulomb potential based on a canonical distribution of virtual photons, resulting in a finite zero-point energy density and addressing the cutoff issue in Lamb shift calculations.

Contribution

It introduces a new model where virtual photon creation follows a canonical distribution, leading to a modified Coulomb potential and finite electromagnetic zero-point energy.

Findings

Modified Coulomb potential: $V(r)=- ze^2 ext{arctan}(m_c r)/(2 ext{pi}^2 r)$

Finite zero-point energy density of electromagnetic field

Addresses the need for a cutoff in Lamb shift calculations

Abstract

The need for a cutoff in the Lamb shift calculation suggests that high-energy virtual photons do not interact with real particles. In this paper, we assume that the creation of virtual photons follows a canonical distribution. As a result, the Coulomb potential is modified to $V(r)=- ze^2\arctan (m_c r)/(2\pi^2 r)$, and the zero-point energy density of the electromagnetic field becomes finite.