Renormalization of the post-Gaussian effective potential

In order to study the effects of renormalization on the variationally calculated φ⁴ effective potential, we employ the Gaussian-effective-potential formalism, nonlinear canonical transformations, and the loop approximation. A quantitative comparison of physically equivalent potentials is carried out in two dimensions. The renormalization procedure in three dimensions, leading after the nonlinear transformation to a manifestly finite energy expectation, is described. Different from finite-dimensional quantum mechanics, the optimization is meaningful only if all divergent sub-graphs generated by the ansatz are identified and renormalized by the bare parameters.