Classical limits of scalar and tensor gauge operators based on the overlap Dirac matrix

It was recently proposed by the second author to consider lattice formulations of QCD in which complete actions, including the gauge part, are built explicitly from a given Dirac operator D. In a simple example of such theory, the gauge action is proportional to the trace of Ginsparg-Wilson operator D chosen to define the quark dynamics. This construction relies on the proposition that the classical limit of lattice gauge operator trD(x,x) is proportional to trF2(x) (up to an additive constant). Here we show this for the case of the overlap Dirac operator using both analytical and numerical methods. 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 results identical to our previous derivation that used a different approach. The corresponding proportionality constants are computed to high precision for a wide range of the negative mass parameter values, and it is verified that they are the same in finite and infinite volumes.