U. D. Jentschura, B. J. Wundt
Superluminal spin-1/2 particles are analyzed under the assumption that the equation of motion is compatible with Lorentz invariance (tachyonic particles). It is found that tachyonic spin-1/2 particles can only be observed in left-handed helicity states, and that tachyonic spin-1/2 antiparticles are always right-handed. This result is independent of the numerical value of the tachyonic mass term, holds even for a tiny tachyonic mass of a few eV and may eventually be verified or falsified by experiments in the long-term future. We propose a superluminal character of the neutrino as an alternative explanation for the lack of a right-handed helicity state. This conclusion is connected with the superluminal Dirac algebra (Gordon identities) for spin-1/2 tachyonic particles. In particular, we derive the decomposition of the superluminal vector and axial vector current into convective and spin parts. Finally, we complement the discussion by giving bispinor solutions for generalized Dirac equations with mixed tachyonic and tardyonic mass terms, of the form m_1 + gamma5*m2, and m1 + i*gamma5*m2. These solutions and corresponding sums over the fundamental spinor solutions may be useful in a wider context.
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http://arxiv.org/abs/1205.0521
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