Non-relativistic Spinning Particle in a Newton-Cartan Background

TL;DR

This paper develops an action for a non-relativistic spinning particle in a Newton-Cartan background, governed by a non-geodesic equation, and explores its symmetries and equations of motion.

Contribution

It introduces a novel action for spinning particles in Newton-Cartan geometry, extending non-relativistic particle models with Grassmann variables and supersymmetry.

Findings

Derived the non-relativistic Papapetrou equation for spinning particles.

Constructed a supersymmetric invariant action in flat space.

Analyzed the particle's equations of motion in a general background.

Abstract

We construct the action of a non-relativistic spinning particle moving in a general torsionless Newton-Cartan background. The particle does not follow the geodesic equations, instead the motion is governed by the non-relativistic analog of Papapetrou equation. The spinning particle is described in terms of Grassmann variables. In the flat case the action is invariant under the non-relativistic analog of space-time vector supersymmetry.