In this paper we explore the problem of antiparticles in DSR1 and k-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 k-Poincare, 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.
Particle and antiparticle sectors in DSR1 and kappa-Minkowski space-time
GALANTE, ANGELO;
2004-01-01
Abstract
In this paper we explore the problem of antiparticles in DSR1 and k-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 k-Poincare, 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.Pubblicazioni consigliate
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