Spinning Particles on Spacelike Hypersurfaces and their Rest-Frame Description

TL;DR

This paper introduces a new model of spinning particles with positive or negative energy on spacelike hypersurfaces, analyzing their dynamics, interactions, and potential quantization within a relativistic framework.

Contribution

It defines a novel class of spinning particles with definite energy signs and studies their dynamics, interactions, and quantization in the context of relativistic hypersurface formalism.

Findings

Spinning particles exhibit nonminimal 'spin-magnetic field' coupling.

Lienard-Wiechert potentials for these particles are derived.

Rest-frame quantization respecting spin structure is discussed.

Abstract

A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. They are the pseudoclassical basis of the positive energy $({1\over 2},0)$ [or negative energy $(0,{1\over 2})$] parts of the $({1\over 2},{1\over 2})$ solutions of the Dirac equation. The study of the isolated system of N such spinning charged particles plus the electromagnetic field leads to their description in the rest-frame Wigner-covariant instant form of dynamics on the Wigner hyperplanes orthogonal to the total 4-momentum of the isolated system (when it is timelike). We find that on such hyperplanes these spinning particles have a nonminimal coupling only of the type "spin-magnetic field" like the nonrelativistic Pauli particles to which they tend in the nonrelativistic limit. The Lienard-Wiechert potentials associated with these charged spinning particles are found. Then, a comment on how to quantize the spinning particles respecting their fibered structure describing the spin structure is done.