Relativistic effect of entanglement in fermion-fermion scattering

We study the properties of entanglement entropy among scattering particles as observed from different inertial moving frames, based on an exemplary QED process $e^+e^-\rightarrow\mu^+\mu^-$. By the explicit calculation of the Wigner rotation, the entanglement entropy of scattering particles is found to be Lorentz invariant. We also study the behavior of the entanglement between spin degrees of freedom for scattering particles in moving frames. This quantity, being found to change with different inertial reference frames, does not exhibit as a Lorentz invariant.