Variational calculations with improved energy functionals in gauge theories

摘要

For a SU(N) Yang-Mills theory, we present variational calculations usinggaussian wave functionals combined with an approximate projection on gaugeinvariant states. The projection amounts to correcting the energy of thegaussian states by substracting the spurious energy associated with gaugerotations. Based on this improved energy functional, we perform variationalcalculations of the interaction energy in the presence of external electric andmagnetic fields. We verify that the ultraviolet behaviour of our approximationscheme is consistent, as it should, with that expected from perturbationtheory. In particular, we recover in this variational framework the standardone-loop beta function, with a transparent interpretation of the screening andanti-screening contributions.