Kinematics of a relativistic particle with de Sitter momentum space

Understand

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.