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This paper was concerned with the spin-momentum correlation insingle-particle quantum states, which is described by the mixed states underLorentz transformations. For convenience, instead of using the superposition ofmomenta we use only two momentum eigen states (p1 and p2) that areperpendicular to the Lorentz boost direction. Consequently, in 2D momentumsubspace we show that the entanglement of spin-momentum in the moving framedepends on the angle between them. Therefore, when spin and momentum areperpendicular the measure of entanglement is not observer-dependent quantity ininertial frame. Likewise, we have calculated the measure of entanglement (byusing the concurrence) and has shown that entanglement decreases with respectto the increasing of observer velocity. Finally, we argue that, Wigner rotationis induced by Lorentz transformations can be realized as controlling operator.

Spin-momentum correlation in relativistic single particle quantum states