Tachyon optics: Kirchhoff identities and superluminal Bragg diffraction

Abstract

The diffraction of superluminal radiation fields in crystal lattices is studied. The negative mass-square of the tachyonic wave modes affects the modulation function of diffraction gratings and the scattering amplitude. The Bragg condition for tachyon diffraction as well as the longitudinal and transversal cross sections are derived. Scalar and vectorial Kirchhoff identities for superluminal Proca fields are obtained from Sommerfeld’s dipole functionals, in analogy to electromagnetic theory. These surface-integral representations of the tachyon potential and the tachyonic field strengths are used to calculate the asymptotic diffracted modes and the intensity ratios. The dependence of the primary and secondary intensity peaks on the tachyon mass is analyzed in the reciprocal lattice, and the conversion of transversal into longitudinal radiation by way of Bragg scattering is explained. Specifically, tachyonic spectral fits are performed to the TeV spectra of three active galactic nuclei, H2356−309, 1ES 1218+304, and 1ES 1101−232, obtained with the imaging atmospheric Cherenkov detectors HESS, MAGIC, and VERITAS. The curvature in the spectral maps of these blazars is shown to be intrinsic, generated by ultra-relativistic electron populations in the galactic nuclei rather than by intergalactic absorption, and is reproduced by a tachyonic cascade fit.