CONVERGENCE PROPERTIES OF THE EQUAL-TIME CONNECTED GREEN-FUNCTION APPROACH FOR TEMPORAL GAUGE SU(2)(2-MILLS THEORY(1) YANG)

The hierarchy of equations of motion for equal-time Green functions in temporal gauge SU(N) Yang-Mills theory is truncated using ail expansi on in terms of connected Green functions. A second hierarchy of constr aint equations arises from Gauss law and can be truncated in a similar way. Within this approximation scheme we investigate SU(2) Yang-Mills theory on a torus in 2 + 1 spacetime dimensions in a finite basis of plane wave stares and focus on infrared and ultraviolet properties of the approach. In all truncation schemes considered up to the 4-point l evel the connected Green function approach is found to be UV divergent and to violate gauge invariance. The problems associated with adiabat ically generating a nonperturbative ground state are discussed as well . (C) 1998 Academic Press.