A Five Dimensional Perspective on Many Particles in the Snyder basis of Double Special Relativity

TL;DR

This paper introduces a five-dimensional Hamiltonian framework for Double Special Relativity, focusing on the Snyder basis, and demonstrates how multi-particle systems exhibit additive energy and momentum, affecting the understanding of composite object masses.

Contribution

It develops a five-dimensional Hamiltonian approach to DSR, extending it from single particles to many particles, and shows additive properties of energy and momentum in this framework.

Findings

Energy and momentum are additive in the multi-particle Snyder basis.

The rest energy of a composite object can be unbounded, unlike single particles.

The method recovers different DSR bases via gauge choices.

Abstract

After a brief summary of Double Special Relativity (DSR), we concentrate on a five dimensional procedure, which consistently introduce coordinates and momenta in the corresponding four-dimensional phase space, via a Hamiltonian approach. For the one particle case, the starting point is a de Sitter momentum space in five dimensions, with an additional constraint selected to recover the mass shell condition in four dimensions. Different basis of DSR can be recovered by selecting specific gauges to define the reduced four dimensional degrees of freedom. This is shown for the Snyder basis in the one particle case. We generalize the method to the many particles case and apply it again to this basis. We show that the energy and momentum of the system, given by the dynamical variables that are generators of translations in space and time and which close the Poincar\'e algebra, are additive magnitudes. From this it results that the rest energy (mass) of a composite object does not have an upper limit, as opposed to a single component particle which does.