Modification of the effective potential of ${\varphi }^4$ theory using the Boltzmann factor

Abstract

The need for a cutoff in the Lamb shift calculation suggests that high-energy virtual photons do not interact with the real particles. In this study, we assume that the creation of high-energy virtual particles is suppressed by a Boltzmann factor $e^{-\beta E}$ and apply this Boltzmann factor to the effective potential of the ${\varphi }^4$ theory. Consequently, the effective potential is transformed into $V(\varphi )=1/4!{\varphi }^4+{\beta }^{-4}\left\{{\varphi }^3{K}_3(\varphi )-{\varphi }^2{K}_2(\varphi )\right\}$. $K_n(x)$ is the modified Bessel function of the second kind of order $n$. We demonstrate that the minimum of the effective potential occurs for $\varphi \ne 0$.

6 pages, 1 figures; v2: section 3 added