The effective potential as an energy density: The one phase region
An explicit formula is given relating the effective potential in a finite volume \(P(\phi)_ 2\) quantum field theory to the expected energy density under the constraint of a fixed average field. In the one phase region, i.e., where the classical potential equals its convex hull and has nonvanishing second derivative, it is shown via a central limit theorem that in the infinite volume limit the effective potential is equal to the constrained energy density, provided \(\hslash\) is sufficiently small.
scientific article; zbMATH DE number 3978102