Effective Hamiltonian for scalar theories in the Gaussian approximation

We use a Gaussian wave functional for the ground state to reorder the Hamiltonian into a free part with a variationally determined mass and the rest. Once spontaneous symmetry breaking is taken into account, the residual Hamiltonian can, in principle, be treated perturbatively. In this scheme we analyze the O (1) and O (2) scalar models. For the O (2)‐theory we first explicitly calculate the massless Goldstone excitation and then show that the one‐loop corrections of the effective Hamiltonian do not generate a mass.