| he present work concerns nonperturbative variational studies of the effective potential beyond the Gaussian effective potential (GEP) approximation. In the Hamiltonian formalism, we study the method of non-linear canonical transformations (NLCT) which allows one to perform variational calculations with non-Gaussian trial states, constructed by nonlinear unitary transformations acting on Gaussian states. We consider in detail a particular transformation that leads to qualitative as well as quantitative improvement over the Gaussian approximation. In particular we obtain a non-trivial correction to the Gaussian mass renormalization. For a general NLCT state, we present formulas for the expectation value of the ;We also report on the development of a manifestly covariant formulation, based on the Euclidian path integral, to construct lower-bound approximations to... |
