Relativistic effect of entanglement in fermion-fermion scattering

TL;DR

This paper investigates how entanglement entropy in fermion-fermion scattering processes behaves under Lorentz transformations, revealing that total entanglement entropy is Lorentz invariant while spin entanglement varies with reference frames.

Contribution

It provides explicit calculations showing Lorentz invariance of entanglement entropy and the frame dependence of spin entanglement in scattering processes.

Findings

Entanglement entropy remains Lorentz invariant.

Spin entanglement depends on the inertial frame.

Explicit Wigner rotation calculations support these results.

Abstract

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.