Convergence Properties of the Equal-Time Connected Green Function Approach for Temporal Gauge SU(2) 2+1 Yang-Mills Theory

Author： Hauser J.M. Cassing W. Leupold S. Thoma M.H.

Publisher： Elsevier

ISSN： 0003-4916

Source： Annals of Physics, Vol.265, Iss.2, 1998-05, pp. : 155-197

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Abstract

The hierarchy of equations of motion for equal-time Green functions in temporal gauge SU(N) Yang-Mills theory istruncated using an expansion in terms of connected Green functions.A second hierarchy of constraint equations arises from Gausslaw and can be truncated in a similar way. Within this approximationscheme we investigate SU(2) Yang-Mills theory on a torusin 2+1 spacetime dimensions in a finite basis of planewave states and focus on infrared and ultraviolet propertiesof the approach. In all truncation schemes considered up tothe 4-point level the connected Green function approach is foundto be UV divergent and to violate gauge invariance. The problemsassociated with adiabatically generating a nonperturbative groundstate are discussed as well. Copyright 1998 Academic Press.