Continuation of: Applications of Gauge Theories to Enhance Numerical Solutions of Mixed Potential Integral Equations.

Abstract : The intention of this research has been to investigate techniques for solving Maxwell's equations under scattering, radiation and propagation conditions by adapting methods recently developed in mathematical physics. During the first few months of this contract we continued the work begun during the previous three years concerning the possibility of substituting the Coulomb gauge for the standard Lorentz gauge in mixed potential integral equation formulations. In this report in Chapter 2 and 3 we present our investigations concerning conduction current invariance under gauge transformation and the implementation of the Coulomb gauge in time domain integral equation analysis. Although it is widely known that the electromagnetic field is invariant under a gauge transformation, to the authors' knowledge no previous proof existed showing current invariance.