The Complex Faraday Tensor for Relativistic Evolution of a Charged Particle in a Constant Field

In this paper, we deflne the complex Faraday tensor FC as an operator represen- tation of the electromagnetic fleld. The electromagnetic stress-energy tensor can be expressed as T = " FCFC 2"0 . We obtain the general solution of the relativistic evolution of a charged particle in a constant fleld by use of FC and its properties. The method of the derivation of this solution is signiflcantly simpler than the ones which appear in the literature. All of the commonly solved special cases can easily be derived from it. We discuss possible interpretation of the complexiflcation of the electromagnetic tensor. We indicate that FC may express the action of the electromagnetic fleld not only upon the charge of an electron but also upon its spin. We conjecture that this representation is more accurate than the standard representation and that a complex 4D space can be deflned to include a description of the evolution of the magnetic moment.