Perturbation theory with a variational basis: The generalized Gaussian effective potential

Abstract

The perturbation theory with a variational basis is constructed and analyzed. The generalized Gaussian effective potential is introduced and evaluated up to second order for self-interacting scalar fields in one and two spatial dimensions. The problem of the renormalization of the mass is discussed in detail. Thermal corrections are incorporated. The comparison between the finite temperature generalized Gaussian effective potential and the finite temperature effective potential is critically analyzed. The phenomenon of the restoration at high temperature of the symmetry broken at zero temperature is discussed.

Variational study of mass generation and deconfinement in Yang-Mills theory

“…While the GEP is a genuine variational method [46,47], several extensions to higher orders have been proposed [56][57][58][59]. The idea of an expansion around the optimized vacuum of the GEP is not new [65] but has not been developed further. Expanding around the optimized massive vacuum of the GEP, the unconventional massive expansion of Refs.…”

Variational perturbation scheme for many-particle systems in the functional integral approach

“…In fact, this concept has already been used in connection with various research interests such as lattice dynamics, relativistic field theories, and quantum mechanics [7][8][9][10][11][12]. However, to the authors' knowledge, it has never been applied to nonrelativistic many-particle systems.…”

From Condensed Matter to QCD: A Journey Through Gauge Theories on Board of a Variational Tool

“…However, being a first-order approximation, the GEP fails to predict any useful result for the fermions of the standard model, because of the minimal gauge interaction that requires a second order graph at least [12,19]. Even the idea of an expansion around the optimized vacuum of the GEP is not new [29] but has not been developed further.…”