The convexity property of the variational approximations to the effective potential is analyzed both in quantum mechanics and in $\lambda {\phi }^4$ field theory. A simple calculational scheme, based on the generalization of the Gaussian functionals subspace, allows one to reproduce this fundamental feature of the exact effective potential to a very high degree of accuracy. A criterion to clarify the occurrence of spontaneous symmetry breaking in the presence of a flat effective potential is proposed.

• Received 23 October 1989

DOI:https://doi.org/10.1103/PhysRevD.41.1948