Gaussian Effective Potential and the Coleman's normal-ordering Prescription : the Functional Integral Formalism

TL;DR

This paper develops a functional integral approach to calculate the Gaussian effective potential for bosonic systems with Fourier-representable potentials, generalizing Coleman's normal-ordering prescription.

Contribution

It introduces a formal generalization of Coleman's normal-ordering within the functional integral framework for a specific class of bosonic systems.

Findings

Gaussian effective potential calculated for systems with Fourier-representable potentials

Normal-ordering prescription extended to functional integral formalism

Framework applicable to a class of bosonic Hamiltonians

Abstract

For a class of system, the potential of whose Bosonic Hamiltonian has a Fourier representation in the sense of tempered distributions, we calculate the Gaussian effective potential within the framework of functional integral formalism. We show that the Coleman's normal-ordering prescription can be formally generalized to the functional integral formalism.