  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 tr D(x,x) is
proportional to tr F.F(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 different approach. The
corresponding proportionality constants are computed to high precision for wide
range of the negative mass parameter values, and it is verified that they are
the same in finite and infinite volumes.
