Modified Coulomb potential with virtual photons following a canonical distribution

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.