On the Equivalence between the Effective Potential and Zero-Point Energy

TL;DR

This paper demonstrates that the effective potential and zero-point energy are equivalent for many geometries and potentials by showing the zero-point ambiguity vanishes using zeta function techniques.

Contribution

It establishes the equivalence of effective potential and zero-point energy through a rigorous zeta function analysis, clarifying previous ambiguities.

Findings

Zero-point ambiguity vanishes for a large class of geometries.

Effective potential and zero-point energy definitions coincide.

An extra term identified earlier disappears with consistent scale parameter introduction.

Abstract

We investigate a possible difference between the effective potential and zero-point energy. We define the zero-point ambiguity (ZPA) as the difference between these two definitions of vacuum energy. Using the zeta function technique, in order to obtain renormalized quantities, we show that ZPA vanishes, implying that both of the above definitions of vacuum energy coincide for a large class of geometries and a very general potential. In addition, we show explicitly that an extra term, obtained by E. Myers some years ago for the ZPA, disappears when a scale parameter $\mu$ is consistently introduced in all zeta functions in order to keep them dimensionless.