Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1997-08-14
Annals Phys. 265 (1998) 155-197
Physics
High Energy Physics
High Energy Physics - Theory
43 pages, LaTeX, 15 PS figures
Scientific paper
10.1006/aphy.1997.5820
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. We study the consequences of restoring the hierarchy of Gauss law constraints and of different momentum cutoffs for the 2- and the 3-point functions. In all truncation schemes considered up to the 4-point level the connected Green function approach is found to be UV divergent and either violating gauge invariance and/or energy conservation. The problems associated with adiabatically generating a perturbed ground state are discussed as well.
Cassing Wolfgang
Hauser J. M.
Leupold Stefan
Thoma Markus H.
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