We explore gauge fields in the functional Schrödinger representation. We first consider perturbatively solving quantum electrodynamics using known free field wave functionals. Failures of ordinary perturbative techniques force us to develop techniques to solve nontrivial functional differential equations. These techniques can also be used for Yang-Mills as we also demonstrate. We regularize QED in a new fashion using functional directional derivatives. This may also be generalized to Yang-Mills. We carry out mass renormalization in QED using wave functionals since no one has explicitly done it before. We briefly look at magnetic flux tubes in the Abelian Higgs model to illustrate renormalization in a variational calculation. We also perform a variational calculation using wave functionals in Yang-Mills to see if quantum fluctuations can produce electric flux tubes.
