Multi-Particle States in Deformed Special Relativity

TL;DR

This paper explores multi-particle states in Deformed Special Relativity, addressing transformation issues by reformulating DSR with field densities, which resolves the soccer-ball problem and impacts predicted effects.

Contribution

It demonstrates that reformulating DSR with field densities resolves transformation mismatches and the soccer-ball problem, leading to revised estimates for observable effects.

Findings

The integrated Noether current does not obey DSR transformations.

Formulating DSR with field densities resolves the soccer-ball problem.

Predicted effects in DSR are many orders of magnitude smaller.

Abstract

We investigate the properties of multi-particle states in Deformed Special Relativity (DSR). Starting from the Lagrangian formalism with an energy dependent metric, the conserved Noether current can be derived which is additive in the usual way. The integrated Noether current had previously been discarded as a conserved quantity, because it was correctly realized that it does no longer obey the DSR transformations. We identify the reason for this mismatch in the fact that DSR depends only on the extensive quantity of total four-momentum instead of the energy-momentum densities as would be appropriate for a field theory. We argue that the reason for the failure of DSR to reproduce the standard transformation behavior in the well established limits is due to the missing sensitivity to the volume inside which energy is accumulated. We show that the soccer-ball problem is absent if one formulates DSR instead for the field densities. As a consequence, estimates for predicted effects have to be corrected by many orders of magnitude. Further, we derive that the modified quantum field theory implies a locality bound.