  There has been considerable recent interest in the Immirzi parameter as a
measure of parity violating effects in the classical theory of gravitation with
fermion coupling. Most recently it was shown that the Immirzi parameter
together with the non-minimal coupling constant of Dirac spinors provides the
measure for parity violating spin-spin interaction terms in the effective field
theory. For complex values of the Immirzi parameter, the resulting effective
field theory yields complex values for the torsion, and a non-unitary effective
field theory that blows up for the special cases $\gamma=\pm i$ where the
gravitational kinetic term is the Ashtekar action. We show that by restricting
ourselves to real values for the torsion, there is a natural set of choice for
the non-minimal coupling constant that yields real and unitary effective field
theory that does not blow up for the special cases $\gamma=\pm i$. We then show
that these particular values for the non-minimal coupling coefficients most
naturally follow from a non-minimal pseudo-kinetic term in the fermion
Lagrangian.
