The Fermionic Entanglement Entropy and Area Law for the Relativistic Dirac Vacuum State

Abstract

We consider the fermionic entanglement entropy for the free Dirac field in a bounded spatial region of Minkowski spacetime. In order to make the system ultraviolet finite, a regularization is introduced. An area law is proven in the limiting cases where the volume tends to infinity and/or the regularization length tends to zero. The technical core of the paper is to generalize a theorem of Harold Widom to pseudo-differential operators whose principal symbols develop a specific discontinuity at a single point.

arXiv comment37 pages, LaTeX, a few typos corrected (published version)

Cited by in corpus (3)

• Notions of Fermionic Entropies of a Causal Fermion System
• Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension
• An enhanced term in the Szegő-type asymptotics for the free massless Dirac operator