Problems and Progress in Covariant High Spin Description

TL;DR

This paper introduces a universal, covariant framework for describing high-spin particles (spin ≥ 1) using second order differential wave equations based on Casimir invariants, avoiding traditional issues.

Contribution

It develops a novel, representation-specific method for high-spin particle description that is free from common pathologies and does not require auxiliary conditions.

Findings

Provides a covariant, second order differential equation framework for high-spin particles.

Uses Casimir invariants of the spin-Lorentz group to construct projectors.

Eliminates pathologies present in traditional high-spin descriptions.

Abstract

A universal description of particles with spins j greater or equal one , transforming in (j,0)+(0,j), is developed by means of representation specific second order differential wave equations without auxiliary conditions and in covariant bases such as Lorentz tensors for bosons, Lorentz-tensors with Dirac spinor components for fermions, or, within the basis of the more fundamental Weyl-Van-der-Waerden sl(2,C) spinor-tensors. At the root of the method, which is free from the pathologies suffered by the traditional approaches, are projectors constructed from the Casimir invariants of the spin-Lorentz group, and the group of translations in the Minkowski space time.