Interplay between Dynamic Systems Described by the Klein-Gordon and Dirac Equations

Abstract

It is shown that in the (1+1)-dimensional space-time the dynamic system, described by the free Klein-Gordon equation, turns to the dynamic system, described by the free Dirac equation, provided the current and the energy-momentum tensor are redefined in a proper way. By means of a change of variables the spinor wave function satisfying the Dirac equation transforms into a scalar wave function satisfying the Klein-Gordon equation. Expressions for the current and the energy-momentum tensor of the Dirac system appear to depend on an arbitrary constant timelike or null vector. It can be interpreted in the sense that the Dirac dynamic system is not relativistic.