Mean spin entanglement of two massive Dirac particles under Lorentz transformations

TL;DR

This paper investigates how Lorentz transformations affect the mean spin entanglement of two massive Dirac particles, revealing a consistent relationship between entanglement measures and Bell inequality violations.

Contribution

It introduces a transformation matrix for spinors under Lorentz transformations and demonstrates the monotonic relationship between concurrence and Bell parameter.

Findings

Monotonic behavior between concurrence and Bell parameter.

Transformation matrix for Dirac spinors under Lorentz transformations.

Consistent relativistic effects on spin entanglement.

Abstract

We have studied the relativistic effects on the mean spin entanglement of two massive Dirac particles using the simultaneous eigen-spinors of the Foldy-Woutheysen mean spin operator and the Dirac Hamiltonian. We have obtained the transformation matrix from the spinor with specific momentum to the spinor with a transformed momentum under an arbitrary Lorentz transformation. Using the transformation matrix we have shown the consistent monotonic behavior between the concurrence and the maximum value of Bell parameter in Bell inequality of transformed spin states.