Spinor Fields

Abstract

A spinor representation of the generalized energy-momentum density 4-vector is proposed, and examples of such representations for various particles and fields are given. This representation corresponds to the classical representation of the particle’s own rotation, which is described by the diagonal matrix of the moment of inertia. The concept of self-angular rotation of a particle is defined as a spatial characteristic of the field, at each point of which there is a local vortex rotation with an angular velocity Ω – a spinor field. The matrix representation of the vortex rotation Ω (spinor) and the values of the components of such a representation are derived from the matrix representation of the Lorentz transformation. The traditional concept of spin-orbit interaction, as the interaction of the magnetic moment of a particle with the magnetic field of orbital motion, is presented as the interaction of a charged particle with a spinor field. Solutions to the problems of particle motion in an external spinor field in the case of a hydrogen-like atom and planetary motion, splitting of the electron energy levels of an atom in an external magnetic field, deflection of a photon by the gravitational field, and representations in metric spaces are presented.