Gaussian effective potential. II. λ${\phi }^4$ field theory

The Gaussian-effective-potential approach is used to explore the physics of λ${\phi }^4$ field theory in 1, 2, 3, and 4 spacetime dimensions. A simple and systematic approach to the renormalization, without explicit regularization, is employed. In four dimensions we find a viable, nontrivial theory arising from a bare coupling constant of a particular negative, infinitesimal form. The theory is ‘‘precarious’’: it is stable in the absence of an ultraviolet cutoff, but unstable when regularized. Perturbation theory is related to this form of the theory, though not straightforwardly. We also discuss particle masses, and the absence of two-particle bound states in ${\phi }^4$ theory.