Quantum theory of synchrotron radiation from charged massless fermions

This work is the first, to the best of our knowledge, to study synchrotron radiation (SR) from a massless charged electron based on the quantum theory of radiation using exact solutions of the Dirac equation in a constant magnetic field. The cases of ($2+1$)-dimensional and ($3+1$)-dimensional quantum electrodynamics are considered separately, and the calculation of synchrotron radiation of conduction electrons in single-layer graphene is presented. A comparative analysis of two types of quantum effects in massive and massless theories of synchrotron radiation is carried out. Analytical expressions obtained for the spectral distribution and total radiation power for all the processes are considered. It is shown that the SR of a massless charged electron is a purely quantum process in both $QE{D}_{2+1}$ and $QE{D}_{3+1}$.