The Gravitational, Electromagnetic, and Vector Meson Fields and the Similarity Geometry

Abstract

It is shown that a special case of the general conformal geometry, called here the similarity geometry, forms the basis for a unitary theory of the gravitational, electromagnetic, and vector meson fields. The field equations are obtained from a simple four-dimensional, gauge invariant variational principle involving the curvature scalar of a basic second rank symmetric similarity tensor ${S}_{\ensuremath{\sigma}\ensuremath{\tau}}$. Since ${S}_{\ensuremath{\sigma}\ensuremath{\tau}}$ is here specialized, there is the possibility of incorporating further fields when the restrictions are removed.