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

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.