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The need for a cutoff in the Lamb shift calculation suggests that high-energyvirtual photons do not interact with real particles. In this paper, we assumethat the creation of high-energy virtual particles is suppressed by a Boltzmannfactor. As a result, the Coulomb potential is modified, and the zero-pointenergy density and one-particle-irreducible self-energy of the scalar field arefinite.

Eliminating ultraviolet divergence in quantum field theory through use of the Boltzmann factor