Massive relativistic particle model with spin from free two-twistor dynamics and its quantization

TL;DR

This paper develops a relativistic particle model with spin derived from two-twistor dynamics, leading to wave equations that describe particles with specific mass, spin, and charge, and generating higher spin field solutions.

Contribution

It introduces a novel 18-dimensional phase space model from two-twistor dynamics, incorporating spin and charge sectors, and derives consistent wave equations for higher spin particles.

Findings

Wave equations for relativistic particles with spin and charge

Generation of higher spin field solutions from wavefunctions

Analysis of constraints and invariant spin projections

Abstract

We consider a relativistic particle model in an enlarged relativistic phase space M^{18} = (X_\mu, P_\mu, \eta_\alpha, \oeta_\dalpha, \sigma_\alpha, \osigma_\dalpha, e, \phi), which is derived from the free two-twistor dynamics. The spin sector variables (\eta_\alpha, \oeta_\dalpha, \sigma_\alpha,\ osigma_\dalpha) satisfy two second class constraints and account for the relativistic spin structure, and the pair (e,\phi) describes the electric charge sector. After introducing the Liouville one-form on M^{18}, derived by a non-linear transformation of the canonical Liouville one-form on the two-twistor space, we analyze the dynamics described by the first and second class constraints. We use a composite orthogonal basis in four-momentum space to obtain the scalars defining the invariant spin projections. The first-quantized theory provides a consistent set of wave equations, determining the mass, spin, invariant spin projection and electric charge of the relativistic particle. The wavefunction provides a generating functional for free, massive higher spin fields.