Variational calculations in gauge theories

We investigate the possibility of using Gaussian trial wave functionals to describe some of the physics in gauge theories. We derive the variational equations and discuss their properties. In the case of the vacuum state we consider a special Gaussian ansatz whose expectation value corresponds to a constant magnetic field and whose kernel is the second variation of the classical energy around this configuration. We discuss the divergences occurring in the quadratic and quartic terms and conjecture that they can be absorbed by a renormalization of the coupling constant. This aspect will be examined in a future publication.