Time-resolved propagation of electromagnetically interacting fermions

The propagation of electromagnetically interacting fermion- antifermion states representing mesons in free space and in medium is studied by means of the coupled time-dependent Dirac equation. This is solved numerically using the staggered leap- frog method on a spatial lattice. The stability of the equation is challenged by the presence of time-retarded potentials generated by the 4-vector, fermionic currents. The known effect of high-frequency oscillations that is inherent in the Dirac equation becomes less pronounced in the presence of mutual interactions. The time-development of the system is evaluated to address its dissociation. Self-interaction that amounts to emission and subsequent absorption of photons is also studied and the effects on wavefunction and mass renormalization are evaluated.