Abstract
The relativistic theory of Cox’s scalar non-point particle with intrinsic structure in the Proca approach in external uniform magnetic and electric fields in the Minkowski space is developed. A generalized Klein–Gordon–Fock equation is derived and is detailed in the presence of uniform magnetic and electric fields. The extension of this formalism to the arbitrary Riemannian space-time background is given. For a special class of curved metrics allowing for the existence of nonrelativistic wave equations, a generalized Schr¨odinger-type quantum mechanical equation for Cox’s particle is derived. This generally covariant formalism is suitable in the presence of external magnetic and electric fields. It is shown that, in the most general form, the extended first-order Proca-like system of tensor equations contains non-minimal interaction terms through the electromagnetic tensor FaB and the Ricci tensor RaB.
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