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It was recently proposed by the second author to consider latticeformulations of QCD in which complete actions, including the gauge part, arebuilt explicitly from a given Dirac operator D. In a simple example of suchtheory, the gauge action is proportional to the trace of Ginsparg-Wilsonoperator D chosen to define the quark dynamics. This construction relies on theproposition that the classical limit of lattice gauge operator tr D(x,x) isproportional to tr F.F(x) (up to an additive constant). Here we show this forthe case of the overlap Dirac operator using both analytical and numericalmethods. We carry out the same analysis also for the tensor component of D,which is similarly related to the field-strength tensor F, and obtain resultsidentical to our previous derivation that used different approach. Thecorresponding proportionality constants are computed to high precision for widerange of the negative mass parameter values, and it is verified that they arethe same in finite and infinite volumes.

Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix