Quantum tachyons

Abstract.

The interaction of superluminal radiation with matter in atomic bound-bound and bound-free transitions is investigated. We study transitions in the relativistic hydrogen atom effected by superluminal quanta. The superluminal radiation field is coupled by minimal substitution to the Dirac equation in a Coulomb potential. We quantize the interaction to obtain the transition matrix for induced and spontaneous superluminal radiation in hydrogen-like ions. The tachyonic photoelectric effect is scrutinized, the cross-sections for ground state ionization by transversal and longitudinal tachyons are derived. We examine the relativistic regime, high electronic ejection energies, as well as the first order correction to the non-relativistic cross-sections. In the ultra-relativistic limit, both the longitudinal and transversal cross-sections are peaked at small but noticeably different scattering angles. In the non-relativistic limit, the longitudinal cross-section has two maxima, and its minimum is located at the transversal maximum. Ionization cross-sections can thus be used to discriminate longitudinal radiation from transversal tachyons and photons.