Extension of the Shirafuji model for Massive Particles with Spin

TL;DR

This paper extends the Shirafuji model to describe massive particles with spin and charge, providing a geometric framework that bridges twistorial and standard particle models, and quantizes it to obtain wavefunctions.

Contribution

The paper introduces a new geometric model for massive spinning charged particles that interpolates between twistorial and standard descriptions, and explicitly quantizes it.

Findings

Wavefunctions explicitly derived for particles with mass, spin, and charge

Spacetime coordinates become non-commutative in the model

Wavefunctions depend on a covariant projection of the spacetime four-vector

Abstract

We extend the Shirafuji model for massless particles with primary spacetime coordinates and composite four-momenta to a model for massive particles with spin and electric charge. The primary variables in the model are the spacetime four-vector, four scalars describing spin and charge degrees of freedom as well as a pair of Weyl spinors. The geometric description proposed in this paper provides an intermediate step between the free purely twistorial model in two-twistor space in which both spacetime and four-momenta vectors are composite, and the standard particle model, where both spacetime and four-momenta vectors are elementary. We quantize the model and find explicitly the first-quantized wavefunctions describing relativistic particles with mass, spin and electric charge. The spacetime coordinates in the model are not commutative; this leads to a wavefunction that depends only on one covariant projection of the spacetime four-vector (covariantized time coordinate) defining plane wave solutions.