Relativistic Spinor Dynamics Inducing the Extended Lorentz-Force-Like Equation

TL;DR

This paper derives a set of Weyl spinor equations in Minkowski space-time that induce an extended Lorentz-force-like equation, incorporating additional degrees of freedom related to classical spin, highlighting the fundamental role of relativistic spinor dynamics.

Contribution

It introduces a novel set of dynamical Weyl spinor equations that induce an extended Lorentz-force-like equation, linking spinor dynamics with classical spin in relativistic physics.

Findings

Derivation of Weyl spinor equations inducing extended Lorentz-force-like dynamics

Inclusion of additional degrees of freedom related to classical spin

Highlighting the fundamental role of relativistic spinor dynamics in physics

Abstract

The special relativistic dynamical equation of the Lorentz force type can be regarded as a consequence of a succession of space-time dependent infinitesimal Lorentz transformations as shown by one of us \cite{buitrago} and discussed in the introduction below. Such an insight indicates that the Lorentz-force-like equation has an extremely fundamental meaning in physics. In this paper we therefore present a set of dynamical Weyl spinor equations {\em inducing} the extended Lorentz-force-like equation in the Minowski space-time. The term extended refers to the dynamics of some additional degrees of freedom that may be associated with the classical spin namely with the dynamics of three space-like mutually orthogonal four-vectors, all of them orthogonal to the linear four-momentum of the object under consideration.