Quantum statistics of superluminal radiation

A statistical quantization of superluminal (tachyon) radiation is introduced. The tiny tachyonic fine structure constant suggests to depart from the usual quantum field theoretic expansions, and to use more elementary methods such as detailed equilibrium balancing of emission and absorption rates. Instead of commencing with an operator interpretation of the wave function, we quantize the time-averaged energy functional and the energy-balance equation. This allows to use different statistics for different types of modes. Transversal superluminal modes are quantized in Bose statistics, longitudinal ones are turned into fermions, resulting in a positive definite Hamiltonian for the radiation field. We discuss the absorptive space structure underlying superluminal quanta and the energy dissipation related to it. This dissipation leads to an adiabatic time variation of the temperature in the bosonic and fermionic spectral functions, gray-body quasi-equilibrium distributions with a dispersion relation adapted to the negative mass-square of the tachyonic modes. The superluminal radiation field couples by minimal substitution to subluminal matter. Adiabatically damped Einstein coefficients are obtained by detailed balancing, as well as emission and absorption rates for tachyon radiation in hydrogenic systems, in particular the possibility of spontaneous emission of superluminal fermionic quanta is pointed out, and time scales for the approach to equilibrium are derived.