Singularity dynamics: Action and Reaction

Abstract

The interaction between singular and regular fields is considered for Lorentz-invariant scalar and vector wave equations. The singular field is generated by a Dirac source term. Its dynamics are deduced from the total field Lagrangian. At non-relativistic speeds, the resulting equations of motion are those of a mass in a scalar potential. Using this method we deduce the relationship between source amplitude (scalar gravitational mass) and dynamic mass (inertial mass). Generalising this method implies Lorentz forces for charge singularities in the electromagnetic field and describes the dynamics and interaction of hypothetical magnetic monopoles.