The physics of gauge transformations

Abstract

A novel approach to classical electromagnetic gauge transformations with an emphasis on the propagation of potentials at finite speeds from charge and current densities is discussed. We consider a new velocity gauge, where the scalar potential propagates at any chosen speed, and the vector potential has a component that propagates at the same speed and another that travels at the finite speed c. Our emphasis on the propagation of the potentials is different from the vector field decomposition of Helmholtz. We discuss two defects of the Helmholtz method and show that our approach corrects them. Our approach enables us to visualize how the potentials propagate in space and see the link between the violation of gauge invariance and the violation of causality and relativity.