Conservation Laws in Doubly Special Relativity

TL;DR

This paper derives the exact conservation laws for energy and momentum in two Doubly Special Relativity theories, which modify Lorentz invariance at high energies, providing potential observational tests for quantum gravity effects.

Contribution

It provides the first exact derivation of energy-momentum conservation laws for composite systems in DSR1 and DSR2 theories, clarifying their nonlinear Lorentz transformations.

Findings

Unique exact conservation laws for DSR1 and DSR2

Strategies for arbitrary nonlinear Lorentz realizations

Potential observational signatures of Lorentz invariance deviations

Abstract

Motivated by various theoretical arguments that the Planck energy (Ep - 10^19 GeV) - should herald departures from Lorentz invariance, and the possibility of testing these expectations in the not too distant future, two so-called "Doubly Special Relativity" theories have been suggested -- the first by Amelino-Camelia (DSR1) and the second by Smolin and Magueijo (DSR2). These theories contain two fundamental scales -- the speed of light and an energy usually taken to be Ep. The symmetry group is still the Lorentz group, but in both cases acting nonlinearly on the energy-momentum sector. Accordingly, since energy and momentum are no longer additive quantities, finding their values for composite systems (and hence finding the correct conservation laws) is a nontrivial matter. Ultimately it is these possible deviations from simple linearly realized relativistic kinematics that provide the most promising observational signal for empirically testing these models. Various investigations have narrowed the conservation laws down to two possibilities per DSR theory. We derive unique exact results for the energy-momentum of composite systems in both DSR1 and DSR2, and indicate the general strategy for arbitrary nonlinear realizations of the Lorentz group.