The Fock-Kemmer approach to precursor shock waves in relativistic field theory

Abstract

We use distribution theory (generalized functions) to extend and justify the Fock-Kemmer approach to the propagation of precursor shock wave discontinuities in classical and quantum field theory. We apply lightcone causality arguments to propose that shock wave singularities in non-linear classical field theories and in Maxwell's equations for responsive media require a form of classical renormalization analogous to Wilson operator product expansions in quantum field theories.