Lorentz-Invariant Formulation of Cherenkov Radiation by Tachyons

Previous treatments of Cherenkov radiation by tachyons have been in error because the prescription employed to cut off the divergent integral over frequency, namely ${\omega }_{max}=\frac{E}{\hslash }$, is not a Lorentz-invariant procedure. The resulting equation of motion for the tachyon is therefore not covariant. The proper procedure requires an extended, deformable distribution of charge and yields a particularly simple form for the tachyon's world line. A simple, covariant equation of motion is derived that describes the motion of a charged tachyon that is emitting Cherenkov radiation. It is shown that Cherenkov radiation by tachyons implies their ultimate annihilation with an antitachyon and demonstrates a disturbing property of tachyons, namely the impossibility of specifying arbitrary Cauchy data even in a purely classical theory.