Classical Mechanics of Spinning Patricle in a Curved Space

TL;DR

This paper models a spinning particle in curved space using Hamiltonian mechanics, showing its equations align with those in general relativity, and discusses potential quantization methods.

Contribution

It introduces a Hamiltonian framework for a spinning particle in curved space, linking classical mechanics with general relativity and exploring quantization approaches.

Findings

Hamilton equations match Papapetrou equations for spinning particles

Provides a Hamiltonian formalism for spinning particles in curved space

Discusses potential methods for quantizing the system

Abstract

An example of mechanical system whose configuration space is direct product of a curved space and the local group of rotations, is presented. The system is considered as a model of spinning particle moving in the space. The Hamiltonian formalism for this system and possible method for its quantization are discussed. It is shown that the Hamilton equations coincide with the Papapetrou equations for spinning test-particle in general relativity.