Phenomenology of the Magueijo-Smolin model of doubly special relativity using the non-relativistic limit of the Dirac equation, spin and Zeeman effect

In this article, we investigate the phenomenology of the Magueijo-Smolin (MS) model of Doubly Special Relativity by examining the non-relativistic (NR) limit of the Dirac equation and its implications for spin dynamics. A deformed Dirac equation is derived within the MS model framework and is used to explore the continuity equation and the NR limit, leading to a deformed Schrödinger-Pauli equation. The effectiveness of this NR limit is compared to the Foldy–Wouthuysen transformation. Additionally, we obtain the classical limit of the deformed Schrödinger-Pauli equation and evaluate the gyromagnetic factor of the Dirac particle. The spin motion equation and a deformed magnetization current are also derived within the MS model framework. Furthermore, using the mass difference between the tau and anti-tau particles induced by the MS model, we establish a lower bound on the parameter κ. The MS model's impact is analyzed in both relativistic and NR systems through the continuity equation, and the anomalous Zeeman effect is extensively studied in this context. This study highlights the influence of the MS model on both relativistic and NR dynamics.