Kinematics of a relativistic particle with de Sitter momentum space

TL;DR

This paper explores the kinematics of a relativistic particle with a deformed phase space where momentum space is modeled as a de Sitter space, deriving its action, symmetries, and worldline parametrization.

Contribution

It provides a detailed derivation of the action, Hamiltonian structure, and equations of motion for a relativistic particle with de Sitter momentum space, including symmetry transformations.

Findings

Explicit formulas for deformed Poincare' group actions

Comparison of deformed and ordinary relativistic kinematics

Insights into parametrization of particle worldlines

Abstract

We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and equations of motion for such free particle. We study the action of deformed relativistic symmetries on the phase space and derive explicit formulas for the action of the deformed Poincare' group. Finally we provide a discussion on parametrization of the particle worldlines stressing analogies and differences with ordinary relativistic kinematics.