Massive Particle Model with Spin from a Hybrid (spacetime-twistorial) Phase Space Geometry and Its Quantization

TL;DR

This paper develops a hybrid phase space model for massive particles with spin and charge, extending the Shirafuji model, and quantizes it to derive wavefunctions with non-commutative spacetime coordinates.

Contribution

It introduces a novel hybrid geometric model bridging twistorial and standard particle models, incorporating spin and charge, and provides explicit quantization results.

Findings

Wavefunctions depend on a single covariant projection of spacetime.

Spacetime coordinates are non-commutative in the model.

Explicit quantization yields relativistic particles with mass, spin, and charge.

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 defining plane wave solutions.