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

• URL: http://arxiv.org/abs/2310.03493v3
• Date: Sun, 20 Oct 2024 05:47:41 GMT
• Title: The Fermionic Entanglement Entropy and Area Law for the Relativistic Dirac Vacuum State
• Authors: Felix Finster, Magdalena Lottner, Alexander V. Sobolev,
• Abstract summary: We consider the fermionic entanglement entropy for the free Dirac field in a bounded spatial region of Minkowski spacetime. An area law is proven in the limiting cases where the volume tends to infinity and/or the regularization length tends to zero.
• Score: 44.99833362998488
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• 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.

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