Nonrelativistic limits of the Klein-Gordon and Dirac equations in the Amelino-Camelia DSR
Jafari N. Shukirgaliyev B.
June 2024Elsevier B.V.
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
2024#853
This paper is devoted to the study of the nonrelativistic limit of Amelino-Camelia doubly special relativity and the corresponding modified Klein-Gordon and Dirac equations. We show that these equations reduce to the Schrödinger equations for the particle and the antiparticle with different inertial masses, however, their rest masses are the same. M. Coraddu and S. Mignemi have studied the nonrelativistic limit of the Magueijo-Smolin doubly special relativity. We compare their results with our study and show that these two models are reciprocal to each other in the nonrelativistic limit. We find that particle and antiparticle masses can be different. These different masses lead to the CPT violation. Also, we will find an upper limit on the photon mass.
Doubly special relativity , Non-relativistic limit , Relativistic quantum mechanics
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Fesenkov Astrophysical Institute, Almaty, 050020, Kazakhstan
Al-Farabi Kazakh National University, Al-Farabi av. 71, Almaty, 050040, Kazakhstan
Center for Theoretical Physics, Khazar University, 41 Mehseti Street, Baku, AZ1096, Azerbaijan
Heriot-Watt International Faculty, Zhubanov University, Aktobe, 030000, Kazakhstan
Energetic Cosmos Laboratory, Nazarbayev University, Astana, 010000, Kazakhstan
Department of Computation and Data Science, Astana IT University, Astana, 010000, Kazakhstan
Fesenkov Astrophysical Institute
Al-Farabi Kazakh National University
Center for Theoretical Physics
Heriot-Watt International Faculty
Energetic Cosmos Laboratory
Department of Computation and Data Science
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