Variational calculations of the effective potential with non-Gaussian trial wave functionals.

Variational calculations of the effective potential, going beyond the Gaussian innthe context of λO 4 theory. Following Polley and Ritschel we use trial wave functionals obtained by a nontrivial unitary operator U=e −isB acting on a Gaussian wave functional. We discuss in detail two cases in which the operator B has the forms (i) B=π 3 , and (ii) B=π R O T 2 , where O isthe field operator and π is its canonical conjugate. [R and T refer to radial and transverse directions in the O(N)-symmetric case.] We calculate the expectation value of the Hamiltonian in the non-Gaussian trial states thus generated, and obtain the optimization equations for the variational-parameter functions of the ansatz