Abstract
Based on early theoretical work on tachyonic fermions we shall study a modification of the Gross–Neveu model in two dimensions. We shall see that the theory results to the dynamical generation of real and imaginary masses. These imaginary masses indicate the possibility that tachyonic solutions (or instabilities) could exist in the theory. The implications of a tachyonic neutrino coming from astrophysical sources are critically discussed. Moreover, we present a toy model that consists of an U(2, 2) invariant Dirac Lagrangian. This theory can have tachyonic masses as solutions. A natural mass splitting between the solutions is a natural outcome of the formalism.
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