The space-time symmetry group of a spin 1/2 elementary particle

TL;DR

This paper explores an extended space-time symmetry group for a relativistic spin 1/2 particle, revealing additional symmetries like dilations and local rotations, and discusses implications for particle properties such as spin and isospin.

Contribution

It identifies a larger symmetry group for Dirac particles, including dilations and local rotations, and links spin and isospin within this framework.

Findings

The symmetry group contains space-time dilations and local rotations.

The group has two Casimir operators: spin and spin projection.

The particle can be modeled as a system with spin and isospin, with possible color states.

Abstract

The space-time symmetry group of a model of a relativistic spin 1/2 elementary particle, which satisfies Dirac's equation when quantized, is analyzed. It is shown that this group, larger than the Poincare group, also contains space-time dilations and local rotations. It has two Casimir operators, one is the spin and the other is the spin projection on the body frame. Its similarities with the standard model are discussed. If we consider this last spin observable as describing isospin, then, this Dirac particle represents a massive system of spin 1/2 and isospin 1/2. There are two possible irreducible representations of this kind of particles, a colourless or a coloured one, where the colour observable is also another spin contribution related to the zitterbewegung. It is the spin, with its twofold structure, the only intrinsic property of this Dirac elementary particle.