Special Relativistic Field Theories in Five Dimensions

Abstract

In view of the current use of a five-dimensional manifold for the development of general relativistic unified field theories, special relativistic theories of pure fields are here expressed in terms of an extra dimension. According to these theories the rest mass of a particle is not an arbitrary parameter, constant under all conditions. It appears in the equations as an operator, although no clue would be expected from a special theory of the eigenvalues of this operator when the particle is moving freely. The Lagrangian densities and equations of motion assume a simpler form than in the usual treatment and the extra elements of the energy tensor which appear may be given a consistent physical significance. The unified vector-pseudo-scalar theory of mesons is a particular case of the fields here considered. The preliminary equations for the description of a pseudo-scalar-vector electromagnetic field are also written down. The pseudo-scalar part cannot be used in general to describe gravitational interaction approximately in special relativity theory.