Abstract:

The Dirac equation describes the relativistic evolution of electrons and positrons. We consider the (time-dependent!) Dirac equation in three dimensions coupled to a potential with Coulomb-type singularities. Motivated by a question from quantum field theory, we prove a propagation of singularities result for this equation and show that singularities are diffracted by the singularities of the potential. If time permits, I will describe how similar techniques can be used to characterize the asymptotic behavior of solutions of this system. This talk is based on joint work with Jared Wunsch as well as work with Bob Booth and Jesse Gell-Redman.