  We consider a mixed system of Dirac fermions in a general
parity-nonconserving theory and renormalize the propagator matrix to all orders
in the pole scheme, in which the squares of the renormalized masses are
identified with the complex pole positions and the wave-function
renormalization (WFR) matrices are adjusted in compliance with the
Lehmann-Symanzik-Zimmermann reduction formalism. We present closed analytic
all-order expressions and their expansions through two loops for the
renormalization constants in terms of the scalar, pseudoscalar, vector, and
pseudovector parts of the unrenormalized self-energy matrix, which is
computable from the one-particle-irreducible Feynman diagrams of the flavor
transitions. We identify residual degrees of freedom in the WFR matrices and
propose an additional renormalization condition to exhaust them. We then
explain how our results may be generalized to the case of unstable fermions, in
which we encounter the phenomenon of WFR bifurcation. In the special case of a
solitary unstable fermion, the all-order-renormalized propagator is presented
in a particularly compact form.
