Variational principle for effective action and prospects of nonlinear optimization

Building upon an analysis of effective versus one-particle irreducible actions by Dannenberg, we show that the Feynman-Jensen variational principle produces a manifestly Lorentz-covariant lower bound on the generating functional of 1PI Green's functions. The well-known gaussian effective action is reproduced with a gaussian trial action and linear transformations of the path-integral variables. The existence of exactly computable nongaussian trial actions, based on nonlinear shear-type transformations, is pointed out. Application to the φ24 effective potential shows a second-order phase transition at λ=1.55. (orig.)