Open AccessParticle and Antiparticle sectors in DSR1 and -Minkowski space-time
Author(s) -
Roberto Aloisio,
J. M. Carmona,
J. L. Cortés,
Angelo Galante,
A. F. Grillo,
F. Méndez
Publication year - 2004
Publication title -
journal of high energy physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.998
H-Index - 261
eISSN - 1126-6708
pISSN - 1029-8479
DOI - 10.1088/1126-6708/2004/05/028
Subject(s) - antiparticle , minkowski space , dispersion relation , mathematical physics , lorentz transformation , dirac equation , physics , mathematics , momentum (technical analysis) , space time , position and momentum space , antipodal point , causal fermion system , energy–momentum relation , quantum mechanics , dirac sea , dirac fermion , fermion , geometry , finance , chemical engineering , lepton , engineering , economics , electron
In this paper we explore the problem of antiparticles in DSR1 and$\kappa$-Minkowski space-time following three different approaches inspired bythe Lorentz invariant case: a) the dispersion relation, b) the Dirac equationin space-time and c) the Dirac equation in momentum space. We find that it ispossible to define a map $S_{dsr}$ which gives the antiparticle sector from thenegative frequency solutions of the wave equation. In $\kappa$-Poincar\'e, thecorresponding map $S_{kp}$ is the antipodal mapping, which is different from$S_{dsr}$. The difference is related to the composition law, which is crucialto define the multiparticle sector of the theory. This discussion permits toshow that the energy of the antiparticle in DSR is the positive root of thedispersion relation, which is consistent with phenomenological approaches.Comment: 15 pages, no figures, some references added, typos correcte
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