Super-radiance from a relativistic source

We construct a model of cooperative superradiant emission from highly relativistic multi-particle source. revise an existing the literature for two-level particle, and it Hamiltonian describing velocity dependent superradiance. adapt standard diagrammatic framework to compute time evolution density operators our Hamiltonian, demonstrate during process departure results calculation methods. In particular, we that so-called vertical photon result is modified by Lorentz factor sample; also introduce set coupled differential equations certain propagators in velocity-dependent small sample framework, which solve numerically via hybrid fourth order Runge-Kutta convolution approach. methods simple case two particles travelling with slightly differing velocities simulated at varying mean $\beta$ factors, evaluate coherence requirements enhanced observer frame. find these become increasingly restrictive higher even context transformations.