A Bekenstein-Type Bound in QFT
Abstract Let B be a spacetime region of width $$2R >0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>R</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , and $$\varphi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>φ</mml:mi> </mml:math> a vector state localized in B . We show that the vacuum relative entropy of $$\varphi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>φ</mml:mi> </mml:math> , on the local von Neumann algebra of B , is bounded by $$2\pi R$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> -times the energy of the state $$\varphi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>φ</mml:mi> </mml:math> in B . This bound is model-independent and rigorous; it follows solely from first principles in the framework of translation covariant, local Quantum Field Theory on the Minkowski spacetime.
Authors
- Roberto Longo (ORCID: https://orcid.org/0000-0001-7923-3226)
Institutions
- University of Rome Tor Vergata (IT)
Publication Details
- Journal
- Communications in Mathematical Physics
- Published
- 2025-04-04
- DOI
- https://doi.org/10.1007/s00220-025-05261-1
- Citations
- 2
- Primary Topic
- Matrix Theory and Algorithms
- Type
- article
- Field-Weighted Citation Impact
- 3.01
Funders
- Agence Nationale de la Recherche
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Centre National de la Recherche Scientifique
- Università degli Studi di Roma Tor Vergata
- Institut Henri Poincaré
- Sorbonne Université