  Renormalization group procedure for effective particles (RGPEP) is applied to
a theory of fermions that interact only through mass mixing terms in their
Hamiltonian. Problems with virtual pair production in vacuum are avoided by
using the front form of Hamiltonian dynamics. Masses and states of physical
fermions emerge at the end of a calculation that is carried out exactly
irrespective of the strength of the mass mixing terms. An a priori infinite set
of renormalization group equations for all momentum modes of fermion quantum
fields is reduced to just one equation for a two-by-two mass matrix. In
distinction from scalars, fermions never become tachyons but appear chirally
rotated when the mass mixing interaction term is sufficiently strong.
