Variational calculations with improved energy functionals in gauge theories - art. no. 116008

For an SU(N) Yang-Mills theory, we present variational calculations using G aussian wave functionals combined with an approximate projection on gauge i nvariant states. The projection amounts to correcting the energy of the Gau ssian states by subtracting the spurious energy associated with gauge rotat ions. Based on this improved energy functional, we perform variational calc ulations of the interaction energy in the presence of external electric and magnetic fields. We verify that the ultraviolet behavior of our approximat ion scheme is consistent, as it should be, with that expected from perturba tion theory. In particular, we recover in this variational framework the st andard one-loop beta function, with a transparent interpretation of the scr eening and anti-screening contributions.