XXV Workshop on Geometric Methods in Physics 2-8.07.2006

Gerald Goldin

Some Variations on Maxwell's Equations

First we review two variations on Maxwell's equations introduced in earlier work---a class of nonlinear Maxwell theories that have a well-defined Galilean limit, and correspondingly generalized Yang-Mills equations (joint work with V. Shtelen), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation (based on joint work with H.-D. Doebner). Then we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges (joint work with G. Ascoli)---an old idea, but one for which we have been unable to find a previous Maxwellian description. Here we define new electric and magnetic fields, whose governing equations separate into two fully relativistic systems: one describing ordinary electromagnetism, and the other describing an overall attractive (or repulsive) long-range force.