About the kinematics of spinning particles

TL;DR

This paper explores the kinematic properties of spinning particles by examining the Lorentz factor's role in defining 4-velocity, deriving a fundamental constraint in a self-consistent manner.

Contribution

It introduces a new perspective on the kinematics of spinning particles by properly incorporating the Lorentz factor into the 4-velocity definition and deriving key constraints.

Findings

New kinematical properties for v^2 in spinning particles

Derivation of the p_mu v^mu = m constraint self-consistently

Insights applicable to Dirac theory and spinning particle models

Abstract

Inserting the correct Lorentz factor into the definition of the 4-velocity v^mu for spinning particles entails new kinematical properties for v^2. The well-known constraint (identically true for scalar particles, but entering also the Dirac theory, and assumed a priori in all spinning particle models) p_mu v^mu = m is here derived in a self-consistent way.