Dirac spinors and tachyon quantization

Abstract

Dirac spinors for spin-1/2 free tachyons are derived from the Dirac and Klein-Gordon equations in terms of the standard helicity representation of the Poincaré group and superluminal transformations (SLTs). It is shown that the proposed theory of second quantization is Lorentz invariant without inverting the spin-statistics relationship and without introducing indefinite pseudotachyonic states. Second quantized theory of spin-1/2 tachyons in the time-energy representation shows that tachyons are localized in time and that the most natural space for the description of tachyons is T4-space. It has been emphasized that on passing from R4-space (bradyons) to T4-space (tachyons) via either, i.e., complex or real SLTs, tachyons behave in T4-space exactly as bradyons do in R4-space. T4-space can be visualized as an internal space for a subluminal observer while R4-space appears as an internal space for a superluminal observer. PACS Nos.: 14.80K, 03.30t