Hyper-entanglement in a relativistic two-body system

Abstract

We characterize the relativistic hyper-entanglement of two interacting massive fermions governed by the Dirac equation. In particular, we show how a certain Lorentz invariant coupling leads to the simultaneous entanglement of the fermionic spin and orbital degrees of freedom. Besides, this notion of hyper-entanglement turns out to be independent of the inertial reference frame. We also describe how this relativistic pairing mechanism leads to a bound fermionic pair which shows an interesting resemblance to a superconducting Cooper pair.