Optimized Rayleigh-Schrödinger Expansion of the Effective Potential

Abstract

An optimized Rayleigh-Schrödinger expansion scheme of solving the functional Schrödinger equation with an external source is proposed to calculate the effective potential beyond the Gaussian approximation. For a scalar field theory whose potential function has a Fourier representation in a sense of tempered distributions, we obtain the effective potential up to the second order, and show that the first-order result is just the Gaussian effective potential. Its application to the $\lambda {\varphi }^4$ field theory yields the same post-Gaussian effective potential as obtained in the functional integral formalism.

Revtex, 8 pages, no figures, revised version with literal changes

References in corpus (3)

• Gaussian Effective Potential and the Coleman's normal-ordering Prescription : the Functional Integral Formalism
• Rayleigh-Schrödinger Perturbation Theory Based on Gaussian Wavefunctional Approch
• A Variational Expansion for the Free Energy of a Bosonic System

Cited by in corpus (2)

• Sine-Gordon Effective Potential beyond Gaussian Approximation
• Rayleigh-Schroedinger-Goldstone variational perturbation theory for many fermion systems