Electrodynamics: A consequence of nonlinear realizations of the Lorentz group

Abstract

Extensions from the representations of the Lorentz group to include local nonlinear diagonal transformations is sufficient to generate, via the covariant derivative, the interaction of minimal coupling. These diagonal realizations are characterized by six functions φ which must satisfy a system of transformation equations. Inequivalent categories of solutions for the φ give rise to different electromagnetic fields. The Dirac monopole and Coulomb potentials follow directly from two different categories of these nonlinear realizations. Within this theory, charge becomes simply the nonlinear counterpart of intrinsic spin for aparticular nonlinear realization of the Lorentz group. Charge is thus placed on equal footing with intrinsic spin in the sense that both phenomena can be described as consequences of our space-time symmetry. Other solutions for the six φ exist, including a spinor. We briefly discuss the possibility that with these other solutions, these realizations could represent some other basic properties of elementary particles.