Generalized Mathisson-Papapetrou-Tulczyjew-Dixon Equations

TL;DR

This paper develops two extended versions of the Mathisson-Papapetrou-Tulczyjew-Dixon equations derived from pseudoclassical Lagrangians, incorporating 'color' degrees of freedom and supersymmetry on Riemann-Cartan spacetime.

Contribution

It introduces novel generalizations of classical spinning particle equations, including color charge and supersymmetric couplings, from a pseudoclassical Lagrangian framework.

Findings

Derived equations include 'color' charge dynamics similar to Wong equations.

Extended equations automatically satisfy the Tulczyjew condition.

Couplings to torsion are modified by supersymmetric fields.

Abstract

We derive two generalizations of Mathisson-Papapetrou-Tulczyjew-Dixon equations from Casalbuoni-Brink-Schwarz type pseudoclassical Lagrangians of Majorana spinors on a Riemann-Cartan spacetime. One has a "color" freedom, which makes the equations of motion also be a generalization of Wong equations. The other is a spinor model coupled with a Rarita-Schwinger field to preserve the supersymmetry. The coupling to the torsion is modified due to the existence of the Rarita-Schwinger field. In both extensions, the Tulczyjew condition is automatically satisfied.