Radiative instability of quantum electrodynamics in chiral matter

Modification of the photon dispersion relation in chiral matter enables 1 -> 2 scattering. As a result, the single fermion and photon states are unstable to photon radiation and pair production respectively. In particular, a fast fermion moving through chiral matter can spontaneously radiate a photon, while a photon can spontaneously radiate a fast fermion and anti-fermion pair. The corresponding spectra are derived in the ultra-relativistic approximation. It is shown that the polarization of the produced and decayed photons is determined by the sign of the chiral conductivity. Impact of a flat thin domain wall on the spectra is computed.