Modification of the effective potential of $ϕ^4$ theory using the Boltzmann factor

DOI Open Access

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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 $e^{-βE}$ and apply this Boltzmann factor to the effective potential of the $ϕ^4$ theory. Consequently, the effective potential is transformed into $V(ϕ) = 1/4!ϕ^4 + β^{-4} \left \{ ϕ^3 K_3(ϕ) -ϕ^2 K_2 (ϕ) \right\}$. $K_n(x)$ is the modified Bessel function of the second kind of order $n$. We demonstrate that the minimum of the effective potential occurs for $ϕ\ne 0$.

6 pages, 1 figures; v2: section 3 added

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