NEW CONFORMAL GAUGING AND THE ELECTROMAGNETIC THEORY OF WEYL

A new eight-dimensional conformal gauging solves the auxiliary field p roblem and eliminates unphysical size change from Weyl's electromagnet ic theory. We derive the Maurer-Cartan structure equations and find th e zero curvature solutions for the conformal connection. By showing th at every one-particle Hamiltonian generates the structure equations we establish a correspondence between phase space and the eight-dimensio nal base space, and between the action and the integral of the Weyl ve ctor. Applying the correspondence to generic flat solutions yields the Lorentz force law, the form and gauge dependence of the electromagnet ic vector potential and minimal coupling. The dynamics found for these flat solutions applies locally in generic spaces. We then provide nec essary and sufficient curvature constraints for general curved eight-d imensional geometries to be in 1-1 correspondence with four-dimensiona l Einstein-Maxwell space-times, based on a vector space isomorphism be tween the extra four dimensions and the Riemannian tangent space. Desp ite part of the Weyl vector serving as the electromagnetic vector pote ntial, the entire class of geometries has vanishing dilation, thereby providing a consistent unified geometric theory of gravitation and ele ctromagnetism. In concluding, we give a concise discussion of observab ility of the extra dimensions. (C) 1998 American Institute of Physics.