Particle and Antiparticle sectors in DSR1 and kappa-Minkowski space-time

TL;DR

This paper investigates antiparticle sectors in DSR1 and κ-Minkowski space-time using three approaches, revealing differences in antipodal mappings and confirming positive antiparticle energies consistent with phenomenology.

Contribution

It introduces a map for antiparticle sectors in DSR1 and κ-Minkowski space-time, clarifies their differences, and confirms positive antiparticle energies within these frameworks.

Findings

Defined a map $S_{dsr}$ for antiparticles in DSR1.

Identified the antipodal map $S_{kp}$ in κ-Poincaré.

Confirmed antiparticle energies are positive roots of the dispersion relation.

Abstract

In this paper we explore the problem of antiparticles in DSR1 and $\kappa$-Minkowski space-time following three different approaches inspired by the Lorentz invariant case: a) the dispersion relation, b) the Dirac equation in space-time and c) the Dirac equation in momentum space. We find that it is possible to define a map $S_{dsr}$ which gives the antiparticle sector from the negative frequency solutions of the wave equation. In $\kappa$-Poincar\'e, the corresponding map $S_{kp}$ is the antipodal mapping, which is different from $S_{dsr}$. The difference is related to the composition law, which is crucial to define the multiparticle sector of the theory. This discussion permits to show that the energy of the antiparticle in DSR is the positive root of the dispersion relation, which is consistent with phenomenological approaches.