Abstract
The hierarchy of equations of motion for equal-time Green functions in temporal gauge SU(N) Yang–Mills theory is truncated using an expansion in terms of connected Green functions. A second hierarchy of constraint 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 states and focus on infrared and ultraviolet properties of the approach. In all truncation schemes considered up to the 4-point level the connected Green function approach is found to be UV divergent and to violate gauge invariance. The problems associated with adiabatically generating a nonperturbative ground state are discussed as well.
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