Higher-order terms in the strong-coupling expansion for the renormalized effective potential

Abstract

This is the third of three papers on the strong-coupling expansion of the renormalized effective potential in $g{\ensuremath{\varphi}}^{4}$ quantum field theory in $d$-dimensional Euclidean space-time. We first assume that the renormalized strong-coupling expansion for the coefficients of the effective potential in the continuum field theory is a series in powers of $\frac{{M}^{4\ensuremath{-}d}}{g}$, where $M$ is the renormalized mass and $g$ is the bare coupling constant. The first term in this series was obtained in the previous paper. Here we estimate the next terms in the series. The results indicate that our assumption is unlikely to be true. Some alternatives are briefly discussed.