a single particle. The von Neumann entropy is invariant in our case because Lorentz symmetry is unitarily implemented in quantum field theory; each creation operator transforms unitarily under the Lorentz group, hence the prescribed reduction of density matrices in Section V will result in Lorentz-invariant von Neumann entropy for whatever resultant reduced density matrix we have. In contradistinction, Lorentz symmetry is not implemented unitarily in non-relativistic treatments of “wavefunctions".

It is known through earlier efforts by others that for a system of two particles in a total pure state, the von Neumann entropy of the reduced density matrix is a good measure of the entanglement. We demonstrated that such a characterization is in fact Lorentz invariant. Although a system of $n$ particles can be similarly parametrized by the Lorentz-invariant von Neumann entropy each of the reduced density matrices, the characterization of entanglement in terms of these $n$ numbers, and especially in the case when the total system is a mixed configuration rather than a pure state, is still not completely clear and merits further studies.

The research for this work has been supported by funds from the National Science Council of Taiwan under Grants No. NSC91-2112-M006-018 and NSC92-2120-M-006-004. We would 