Optimized post Gaussian approximation in the background field method
We have extended the variational perturbative theory based on the back ground field method to include the optimized expansion of Okopinska and the post Gaussian effective potential of Stansu and Stevenson. This new method provides much simpler way to compute the correction terms to the Gausssian effective action (or potential). We have also renormalized the effective potential in 3+1 dimensions by introducing appropriate counter terms in the lagrangian
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. {copyright} {ital 1997} {ital The American Physical Society}
Cluster expansion approach to the effective potential in Φ2+14-theory
We apply a truncated set of dynamical equations of motion for connected equal-time Green functions up to the 4-point level to the investigation of spontaneous ground state symmetry breaking in Φ2+14 quantum field theory. Within our momentum space discretization we obtain a second order phase transition as soon as the connected 3-point function is included. However, an additional inclusion of the connected 4-point function still shows a significant influence on the shape of the effective potential and the critical coupling.