Comparison of the nonrelativistic limit of Amelino-Camelia and MS Doubly Special Relativity

This paper is devoted to the study of the nonrelativitic limit of Amelino-Camelia Doubly Special Relativity, and the corresponding modified Klein-Gordon and Dirac equations. We show that these equations reduce to the Schrodinger 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 recently the non relativistic 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 nonrelativitic limit. The different inertial masses also leads to the CPT violation.