Covariant hamiltonian spin dynamics in curved space-time

TL;DR

This paper develops a covariant Hamiltonian framework for describing spinning particles in curved space-time, providing new insights into their dynamics, constants of motion, and extensions including spin-gravity interactions.

Contribution

It introduces a covariant Hamiltonian approach for spin dynamics in curved space-time, including minimal and non-minimal models with conserved quantities.

Findings

Constructed constants of motion for minimal Hamiltonian

Analyzed spin dynamics in Schwarzschild space-time

Extended Hamiltonian to include gravitational Stern-Gerlach force

Abstract

The dynamics of spinning particles in curved space-time is discussed, emphasizing the hamiltonian formulation. Different choices of hamiltonians allow for the description of different gravitating systems. We give full results for the simplest case with minimal hamiltonian, constructing constants of motion including spin. The analysis is illustrated by the example of motion in Schwarzschild space-time. We also discuss a non-minimal extension of the hamiltonian giving rise to a gravitational equivalent of the Stern-Gerlach force. We show that this extension respects a large class of known constants of motion for the minimal case.