Nonperturbative treatment of the functional Schrödinger equation in QCD

Use of the functional Schrödinger equation in QCD is complicated by the need to maintain gauge invariance at the same time one is dealing with nonperturbative effects (at least at long distances). Moreover, asymptotic freedom must be recovered at short distances. In this paper we show how to set up and solve a set of Ward identities which ensure gauge invariance of the wave functional, which can then be parametrized simply and used with various nonperturbative algorithms (e.g., variational). Parametrizations are found both for the vacuum wave functional and for $J^{\mathrm{PC}}$ ${=0\mathrm{}}^{\pm +}$ quantum soliton states of QCD. A nonperturbative algorithm, based on the observation that a wave functional is really a partition function in the presence of a special kind of source, is set up and applied; this algorithm is based on dressed-loop expansions of partition functions. One recovers this way some earlier results found from the study of Schwinger-Dyson equations, plus some new results concerning the $0^{\mathrm{-}+}$ soliton, whose wave functional involves the Chern-Simons secondary class function.