Gerald Goldin
Some Variations on Maxwell's Equations
First we review two variations on Maxwell's equations introduced in earlier worka class of nonlinear Maxwell theories that have a welldefined Galilean limit, and correspondingly generalized YangMills 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) longrange
force.
