  Renormalization group procedure for effective particles is applied to the
model quantum theory of free fermions to which one adds an interaction in the
form of a mass mixing term. If one used a standard approach based on the
instant form of dynamics, the theory would suffer from a generic vacuum problem
caused by a divergent production of virtual quanta out of a bare vacuum and it
would require an adjustment of its degrees of freedom to the added interaction
term before quantization, considered a means of avoiding the quantum vacuum
problem. In the effective particle approach, the quantum vacuum problem is
dealt with instead by using the front form of dynamics, where the pair
production is excluded by momentum conservation. The corresponding Hamiltonian
includes mass parameters through constraint equations while the required
quantum field operators are constructed independently of all mass parameters,
including the parameters that appear in the added mass mixing interaction term.
Then the masses and states of physical fermions emerge at an end of the
non-perturbative calculation that is carried out entirely in one and the same
interacting quantum theory with a trivial vacuum and no quantization
adjustment. An a priori infinite set of renormalization group equations for all
momentum modes of fermion fields is reduced to just one equation for a
two-by-two mass squared matrix, thanks to 7 kinematical symmetries of the front
form (the instant form has only 6). For strong mass mixing interactions, the
fermion model solutions qualitatively differ from the analogous, earlier found
boson model solutions by the absence of tachyons.
