Spinor extended Lorentz-force like equations as consequence of a spinorial structure of space-time

TL;DR

This paper derives Lorentz-force-like equations from a spinorial perspective, revealing a fundamental connection between spinor structures and electromagnetic dynamics in space-time.

Contribution

It introduces a spinorial derivation of Lorentz-force equations, incorporating additional degrees of freedom linked to intrinsic spin and SU(2) symmetry.

Findings

Derivation of spinor-based Lorentz-force equations

Geometric representation of electromagnetic field tensor in spinor form

Identification of spin-related degrees of freedom with SU(2) generators

Abstract

As previously shown, 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 boosts and rotations. This insight indicate that the Lorentz-Force-like equation has a fundamental meaning in physics. We show how this result may be spinorially obtained starting out out from the application of an infinitesimal element of SL(2,C) to the individual spinors, which are regarded here as being more fundamental objects than four-vectors. In this way we get a set of new dynamical spinor equations inducing the extended Lorentz-Force-like equation in the Minkowski space-time and geometrically obtain the spinor form of the electromagnetic field tensor. The term extended refers to the dynamics of some additional degrees of freedom that may be associated with the intrinsic spin, namely, with the dynamics of three spacelike mutually orthogonal four-vectors, all of them orthogonal to the linear four-momentum of the object under consideration that finally, in the particle's proper frame. are identified with the generators of SU(2).