Diffusive synchrotron radiation from relativistic shocks in gamma-ray burst sources

The spectrum of electromagnetic emission generated by relativistic electrons scattered on small-scale random magnetic fields, implied by current models of the magnetic field generation in the gamma-ray burst sources, is considered. The theory developed includes both perturbative and nonperturbative versions and therefore suggests a general treatment of the radiation in an arbitrary small-scale random field. It is shown that a general treatment of the random nature of the small-scale magnetic field, as well as angular diffusion of the electrons due to multiple scattering by magnetic inhomogeneities (i.e., nonperturbative effects), gives rise to a radiation spectrum that differs significantly from the so-called "jitter" spectrum. The spectrum of diffusive synchrotron radiation seems to be consistent with the low-energy spectral index distribution of the gamma-ray bursts.