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