The N = 1 Supersymmetric Wong Equations and the Non-Abelian Landau Problem

TL;DR

This paper extends the classical and quantum description of a charged spinning particle in a non-abelian gauge field to include N=1 supersymmetry, providing a framework for analyzing the supersymmetric non-abelian Landau problem.

Contribution

It introduces a supersymmetric Lagrangian formulation for a charged particle with spin in non-abelian fields and applies it to the supersymmetric non-abelian Landau problem.

Findings

Spectrum consistent with supersymmetry

Canonical quantization achieved in a specific gauge

Extension of classical equations to N=1 supersymmetry

Abstract

A Lagrangian formulation is given extending to N = 1 supersymmetry the motion of a charged point particle with spin in a non-abelian external field. The classical formulation is constructed for any external static non-abelian SU(N) gauge potential. As an illustration, a specific gauge is fixed enabling canonical quantization and the study of the supersymmetric non-abelian Landau problem. The spectrum of the quantum Hamiltonian operator follows in accordance with the supersymmetric structure.