Lorentz transformations that entangle spins and entangle momenta

Simple examples are presented of Lorentz transformations that entangle the spins and momenta of two particles with positive mass and spin $1∕2$. They apply to indistinguishable particles, produce maximal entanglement from finite Lorentz transformations of states for finite momenta, and describe entanglement of spins produced together with entanglement of momenta. From the entanglements considered, no sum of entanglements is found to be unchanged.

Figure 1

Values of the velocity $v$ of the Lorentz transformation and the momentum-to-mass ratio $\mid \mathbf{p}\mid ∕m$ that give $\pi ∕4$ for the angle $\varphi$ of the Wigner rotation.

Figure 2

The concurrence $C\left({\rho }^{\Lambda }\right)$ as a function of $v$ for $\mid \mathbf{p}\mid ∕m=10$.