A Universal Model of D=4 Spinning Particle

TL;DR

This paper introduces a comprehensive model for D=4 spinning particles that unifies massive, massless, and helicity cases, with a detailed quantum and classical analysis including interactions with electromagnetic and gravitational fields.

Contribution

It constructs a universal Lagrangian model for D=4 spinning particles on a manifold with a sphere, encompassing various particle types and providing a consistent quantum framework.

Findings

Unified description of massive, massless, and helicity particles.

Explicit quantum wave function representation on R^{3,1} x S^2.

Inclusion of consistent electromagnetic and gravitational interactions.

Abstract

A universal model for D=4 spinning particle is constructed with the configuration space chosen as ${\bf R}^{3,1}\times S^2$, where the sphere corresponds to the spinning degrees of freedom. The Lagrangian includes all the possible world--line first order invariants of the manifold. Each combination of the four constant parameters entering the Lagrangian gives the model, which describes the proper irreducible Poincar\'e dynamics both at the classical and quantum levels, and thereby the construction uniformly embodies the massive, massless and continuous helicity cases depending upon the special choice of the parameters. For the massive case, the connection with the Souriau approach to elementary systems is established. Constrained Hamiltonian formulation is built and Dirac canonical quantization is performed for the model in the covariant form. An explicit realization is given for the physical wave functions in terms of smooth tensor fields on ${\bf R}^{3,1}\times S^2$. One-parametric family of consistent interactions with general electromagnetic and gravitational fields is introduced in the massive case. The spin tensor is shown to satisfy the Frenkel-Nyborg equation with arbitrary fixed gyromagnetic ratio in a limit of weakly varying electromagnetic field.