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

TL;DR

This paper extends the Fock-Kemmer approach using distribution theory to analyze shock wave discontinuities in classical and quantum fields, proposing a renormalization method akin to Wilson expansions.

Contribution

It introduces a distribution-theoretic extension of the Fock-Kemmer approach and links shock wave singularities to a classical renormalization process.

Findings

Distribution theory justifies Fock-Kemmer approach

Shock singularities relate to a classical renormalization

Lightcone causality constrains shock wave behavior

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.