One and two spin-1/2 particle systems under the Lorentz transformations

Lorentz transformation (LT) was used to link two inertial frames, consisted of moving and lab frames. In addition, the effects of LT on the states of two and one spin-½ particle systems are addressed. Throughout the paper, we only consider two spin operators including Czachor's and the Pauli spin operators. It is shown that the system's state predictions made by Pauli spin operator for one spin-½ particle systems is better than that of made by Czachor's spin operator. Thereinafter, we focused on entangled systems consisted of two spin-½ particles moving away from each other and the treatment of system state under Lorentz transformation was studied .We also use both Pauli and Czachor's operators to build the Bell's operator. Additionally, we address the behavior of Bell's inequality under LT and compare the results made by considering Pauli's operator with that of from Czachor's spin operator. In the last part, some results of considering the Pauli-Lubanski spin operator are also addressed.