Variational calculations with improved energy functionals in gauge theories

For an $\mathrm{SU}(N)$ Yang-Mills theory, we present variational calculations using Gaussian wave functionals combined with an approximate projection on gauge invariant states. The projection amounts to correcting the energy of the Gaussian states by subtracting the spurious energy associated with gauge rotations. Based on this improved energy functional, we perform variational calculations of the interaction energy in the presence of external electric and magnetic fields. We verify that the ultraviolet behavior of our approximation scheme is consistent, as it should be, with that expected from perturbation theory. In particular, we recover in this variational framework the standard one-loop beta function, with a transparent interpretation of the screening and anti-screening contributions.