TITLE:
Problems with the Klein-Gordon Theory
AUTHORS:
Eliahu Comay
KEYWORDS:
Classical Electrodynamics, Dirac Theory, Klein-Gordon Theory, The Continuity Equation
JOURNAL NAME:
Open Access Library Journal,
Vol.10 No.8,
August
15,
2023
ABSTRACT: The electromagnetic domain comprises two kinds of physical objects—electromagnetic fields and electrically charged particles. Therefore, the structure of a comprehensive electromagnetic theory is a coherent union of two theories. One theory describes electromagnetic fields, and the second theory describes electrically charged particles. An obvious requirement says that a comprehensive electromagnetic theory must be a coherent union of a theory of electromagnetic fields and a theory of electrically charged particles. The continuity equation is a well-known example showing how Maxwell equations of the electromagnetic fields impose a constraint on a theory that describes the time evolution of a charged particle. The novelty of this work is its proof that the continuity equation is not a unique example. Namely, the Maxwell theory of electromagnetic fields imposes other constraints on a theory of an electric charge. This work shows that the classical theory as well as the Dirac theory of a spin-1/2 charged quantum particle provide a coherent electromagnetic theory. In contrast, new problems arise in the Klein-Gordon theory of a charged spin-0 quantum particle.