Dynamical Equations of Spinning Particles: Feynman's Proof

TL;DR

This paper extends Feynman's derivation of equations of motion to spinning particles, revealing their interactions with electromagnetic and gravitational fields, and deriving corrections to Lorentz force equations.

Contribution

It introduces a novel derivation of spinning particle dynamics, including interactions with fields and corrections to classical equations, expanding Feynman's original framework.

Findings

Spinning particles interact with electromagnetic and gravitational fields.

Re-derivation of Papapetrou's equations in conformal gravity.

Identification of spin-related corrections to Lorentz force equations.

Abstract

In this letter, we discuss the extension of Feynman's derivation of the equation of motion to the case of spinning particles. We show that a spinning particle interacts only with the electromagnetic and gravitational fields. In the absence of the electromagnetic interactions, we rederive Papapetrou's equations for spinning particles in the background of the conformal gravity. We also find that the effect of spin coupled to non-constant electromagnetic fields leads to further corrections to the Lorentz force equations. Some discussions of these results are given at the end.