Generalized relativistic kinematics in Poincar\'e-invariant models

TL;DR

This paper explores how deforming Poincaré invariance while preserving its algebra affects relativistic kinematics, revealing that boost actions remain unchanged while momentum addition laws become flexible, with applications to doubly special relativity and noncommutative geometry.

Contribution

It demonstrates that certain deformations of Poincaré invariance preserve the algebra but alter phase space actions, providing new insights into relativistic kinematics.

Findings

Boost actions on two-particle states are unaffected by the deformation.

Momentum addition laws are largely arbitrary under the deformation.

Hopf-algebra methods yield equivalent results to other approaches.

Abstract

Assuming the validity of the relativity principle, we discuss the implications on relativistic kinematics of a deformation of the Poincar\'e invariance that preserves the Poincar\'e algebra, and only modifies its action on phase space in a Lorentz-invariant way. We show that, in contrast to the case where the Poincar\'e algebra is deformed, the action of boosts on two-particle states is not affected, while the addition law of momenta is to a large extent arbitrary. We give some nontrivial examples of this arising from doubly special relativity and noncommutative geometry and show that Hopf-algebra methods give equivalent results.