Relativistic kinematics beyond Special Relativity

TL;DR

This paper explores how the relativity principle constrains modifications to special relativity when considering high-energy scale effects, deriving the most general form of such modifications consistent with relativity.

Contribution

It derives the constraints between deformation coefficients of composition law, dispersion relation, and transformation laws in a momentum expansion beyond special relativity.

Findings

Relativity principle constrains the form of deformed composition laws.

Modification of the composition law determines the dispersion relation.

Provides the most general relativistic modifications at leading order in 1/M.

Abstract

In the context of departures from Special Relativity written as a momentum power expansion in the inverse of an ultraviolet energy scale M, we derive the constraints that the relativity principle imposes between coefficients of a deformed composition law, dispersion relation, and transformation laws, at first order in the power expansion. In particular, we find that, at that order, the consistency of a modification of the energy-momentum composition law fixes the modification in the dispersion relation. We therefore obtain the most generic modification of Special Relativity that preserves the relativity principle at leading order in 1/M.