  It is suggested that charged tachyons of extremely large mass M could not
only contribute to the dark matter needed to fit astrophysical observations,
but could also provide an explanation for gamma ray bursts and ulta high energy
cosmic rays. The present paper defines a quantum field theory of tachyons,
particles similar to ordinary leptons, but with momenta larger than energy. The
theory is invariant under the full CPT transformation, but separately violates
P and T invariance. Micro causality is broken for space-time intervals smaller
than 1/M, but is effectively preserved for larger separations. Charged
fermionic, rather than charged scalar tachyons are considered in order to
minimize the probability of Cerenkov-like radiation by the tachyon, thereby
permitting a high energy tachyon to retain its energy over galactic distances.
Topics treated include the choice and Schwinger Action Principle variations of
an appropriate Lagrangian, spinorial wave functions, relevant Green's
functions, a functional description of an S-Matrix and generating functional,
and a variety of interesting kinematical processes, including photon emission
and reabsorption, and relevant annihilation and scattering effects. A version
of Ehrenfest's theorem is developed, in order to provide a foundation for a
classical description of charged tachyons in an external electromagnetic field.
Applications are then made to three outstanding astrophysical puzzles : dark
matter, gamma ray bursts and ultra high energy cosmic rays.
