A new 2d-dim gauging of the conformal group of a d-dim spacetime eliminates problems associated with the corresponding d-dim gaugings, while removing unphysical effects of Weyl's electromagnetic theory. We find the flat solutions and show a 1-1 correspondence between phase space and the 2d-dim base space, implying a local correspondence between general curved 2-dimensional gauge theories and phase space. We provide an action for the curvatures which is extremal when the solutions are in 1-1 correspondence with d-dimensional Einstein-Maxwell spacetimes. The entire class of geometries has vanishing dilation, thereby providing a consistent unified geometric theory of gravitation and electromagnetism. The gauge dependence of the electromagnetic vector potential and minimal coupling follow automatically, while the extremum of the integral of the Weyl vector leads directly to the Lorentz force law.
19th Texas Symposium on Relativistic Astrophysics and Cosmology
- Pub Date:
- December 1998