SLOWER-THAN-LIGHT SPIN-1 2 PARTICLES ENDOWED WITH NEGATIVE MASS SQUARED/

Extending in a straightforward way the standard Dirac theory, we study a quantum mechanical wave equation describing free spinning particles - which we propose to call Pseudotachyons (PT's) - which behave like tachyons in the momentum space (p(2) = m(2)), but like subluminal part icles (upsilon < c) in the ordinary space. This is allowed since, as i t happens in every quantum theory for spin-1/2 particles, the momentum operator, -i del, (that is conserved), and the velocity operator alph a, (that is not), are independent operators, which refer to independen t quantities: (p) over cap not equal <m(upsilon)over cap>. As a conseq uence, at variance with ordinary Dirac particles, for PT's the average velocity <(upsilon)over bar> = [psi(dagger)alpha psi]/[psi(dagger)psi ] is not equal to the classical velocity upsilon(cl) = p/epsilon, but actually to the velocity ''dual'' of upsilon(cl):epsilon p/p(2). Being reciprocal of \upsilon(cl)\, the speed of PT's is therefore smaller t han the light speed. Since a lot of experimental data seems to involve a negative mass squared for neutrinos, we suggest that these particle s might be PT's, travelling, because of their very small mass, at subl uminal speeds very close to the light one. The present theory is shown to be separately invariant under the C, P, T transformations; the cov ariance under Lorentz transformations is also proven. Furthermore, we derive the kinematical constraints linking 4-impulse, 4-velocity and 4 -polarization of free PT's.