Lorentz-Invariant Formulation of Cherenkov Radiation by Tachyons

Lienard-Wiechert potentials for charged tachyons and several remarks on the tachyon Cherenkov radiation

“…It is interesting that the Sommerfeld formula predicts the rate of the energy loss due to superluminal electron vacuum radiation which is close to the results of modern calculations for the Cherenkov radiation by a finite-size, "spherically symmetric" charged tachyon, see [22,23,24]. Note, it is rather high, but one can expect that such a radiation will be strongly suppressed in a high energy range (for the photon energies comparable with the energy of the tachyon) after introduction of a longitudinal tachyon form-factor [25] (see also Appendix B), and due to quantum selection rules [1].…”

Un-renormalized classical electromagnetism

“…With reference to (27) it is seen that the 0 th and 2 nd (the time and x 2 -direction) components of the force are automatically zero, which is a predictable consequence of the symmetry of the configuration. This leaves only x 1 component of the force to be resolved.…”

“…As a consequence of the latter only terms that are even in survive the sum. Using (27) let us denote the parity of the scalar products in ( 28) by the subscripts o and e, corresponding respectively to odd and even:…”

“…The total energy is then given as the sum. In the case that the motion is given by (18) and the scalar products are (27), the energy is…”

“…See [26] for a supporting calculation. Wimmel & Jones [27,28] later re-analyzed the production of Cerenkov radiation, replacing Sommerfeld's model of a rigid finite-sized electron (introduced to provide a cutoff for the radiation) with a relativistically-correct variable form, to achieve a finite relativistically-invariant expression for the power loss. But there were features of the result that led Wimmel to conclude that something was wrong with the whole approach.…”