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.

中文翻译：

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Amelino-Camelia DSR 中 Klein-Gordon 和 Dirac 方程的非相对论极限


本文致力于研究Amelino-Camelia双重狭义相对论的非相对论极限以及相应的修正的Klein-Gordon和Dirac方程。我们证明这些方程可简化为具有不同惯性质量的粒子和反粒子的薛定谔方程，但它们的静止质量相同。 M. Coraddu 和 S. Mignemi 研究了 Magueijo-Smolin 双重狭义相对论的非相对论极限。我们将他们的结果与我们的研究进行了比较，并表明这两个模型在非相对论极限上是互易的。我们发现粒子和反粒子的质量可能不同。这些不同的质量导致了 CPT 违规。此外，我们还会找到光子质量的上限。