  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.
