Euclidean continuation of the Dirac fermion

We have found a one-complex-parameter family of Dirac actions which interpolates between the Minkowski and a Euclidean Dirac action. The interpolating action is invariant under the ``interpolating Lorentz transformations.'' The resultant Euclidean action is Hermitian and SO(4) invariant. There is no doubling of degrees of freedom of the Dirac fermion and no contradiction between the SO(4) invariance and the Hermiticity property of the Euclidean propagator. The Euclidean theory so obtained also satisfies the Osterwalder-Schrader positivity condition.