Crucial Dependence of ``Precarious'' and ``Autonomous'' phi^4s Upon the Normal-ordering Mass

TL;DR

This paper investigates how the existence of certain phi^4 quantum field theories depends critically on the choice of normal-ordering mass, revealing specific conditions for their viability in (3+1) dimensions.

Contribution

It demonstrates that precarious and autonomous phi^4 theories in (3+1) dimensions require the normal-ordering mass to match classical masses at specific vacua, clarifying their dependence on renormalization parameters.

Findings

Precarious and autonomous phi^4s exist only when the normal-ordering mass equals classical masses.

The existence conditions differ between symmetric and asymmetric vacua.

The Gaussian wave-functional approach effectively reveals these dependencies.

Abstract

Using the Gaussian wave-functional approach with the normal-ordering renormalization prescription, we show that for the (3+1)-dimensional massive lambda phi^4 theory, ``precarious'' and ``autonomous'' phi^4s can exist if and only if the normal-ordering mass is equal to the classical masses at the symmetrc and asymmetric vacua, respectively.