Spin-momentum correlation in relativistic single particle quantum states

TL;DR

This paper investigates how Lorentz transformations affect spin-momentum entanglement in single-particle quantum states, showing that entanglement depends on the observer's frame and decreases with velocity, with Wigner rotation acting as a control operator.

Contribution

It introduces a simplified model using two momentum eigenstates to analyze spin-momentum entanglement under Lorentz boosts, revealing observer-dependent entanglement behavior.

Findings

Entanglement depends on the angle between spin and momentum.

Entanglement decreases as observer velocity increases.

Wigner rotation can be used as a controlling operator.

Abstract

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