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These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature.
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R. Haag and D. Kastler, “An Algebraic Approach To Quantum Field Theory,” J. Math. Phys. 5
1964
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H. Epstein, V. Glaser and A. Jaffe, “Nonpositivity of the Energy Density in Quantized Field Theories,” Nuovo Cim. 36
1965
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W. Rindler, “Kruskal Space and the Uniformly Accelerated Frame,” Am. J. Phys. 34
1966
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R. T. Powers, “Representations Of Uniformly Hyperfinite Algebras And Their Associated von Neumann Rings,” Ann. of Math. 86
1967
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H. Araki and E. J. Woods, “A Classification Of Factors,” Publ. RIMS, Kyoto Univ. Ser. A. 3
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H. J. Borchers, “On the Converse of the Reeh-Schlieder Theorem,” Commun. Math. Phys. 10
1968
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P. R. Halmos, “Two Subspaces,” Trans. Amer. Math. Soc. 144
1969
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H. Roos, “Independence of Local Algebras in Quantum Field Theory,” Commun. Math. Phys. 16
1970
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M. Reed and B. Simon, Methods of Modern Mathematical Physics, I: Functional Analysis
1972
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E. H. Lieb, “Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture,” Adv. Math. 11
1973
Cited alongside, same era.
H. Araki, “Relative Hamiltonian for Faithful Normal States Of A Von Neumann Algebra,” Publ. RIMS, Kyoto Univ. 9
1973
Cited alongside, same era.
D. Buchholz, “Product States for Local Algebras,” Commun. Math. Phys. 36
1974
Cited alongside, same era.
H. Araki, “Some Properties Of Modular Conjugation Operator of Von Neumann Algebras and a Noncommutative Radon-Nikodym Theorem With A Chain Rule,” Pacific J. Math. 50
1974
Cited alongside, same era.
H. Araki, “Inequalities in Von Neumann Algebras,” Les rencontres physiciens-mathématiciens de Strasbourg, RCP25 22
1975
Cited alongside, same era.
K. Fredenhagen, K. H. Rehren, and B. Schroer, “Superselection Sectors with Braid Group Statistics and Exchange Algebra, I. General Theory,” Commun. Math. Phys 125
1989
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R. Haag, Local Quantum Physics
1992
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M. Srednicki, “Entropy and Area,” Phys. Rev. Lett. 71
1993
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L. Susskind and J. Uglum, “Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory,” Phys. Rev. D50
1994
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M. McGuigan, “Finite Black Hole Entropy and String Theory,” Phys. Rev. D50
1994
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C. G. Callan, Jr. and F. Wilczek, “On Geometric Entropy,” Phys. Lett. B333
1994
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1975
Cited alongside, same era.
R. Figari, R. Hoegh-Krohn, and C. R. Nappi, “Interacting Relativistic Boson Fields In The De Sitter Universe With Two Space-Time Dimensions,” Commun. Math. Phys. 44
1975
Cited alongside, same era.
H. Araki, “Relative Entropy of States of von Neumann Algebras,” Publ. RIMS, Kyoto Univ. 11
1976
Cited alongside, same era.
J. Bisognano and E. H. Wichmann, “On The Duality Condition For Quantum Fields,” J. Math. Phys. 17
1976
Cited alongside, same era.
W. G. Unruh, “Notes On Black-Hole Evaporation,” Phys. Rev. D14
1976
Cited alongside, same era.
S. W. Hawking, “Action Integrals And Partition Functions In Quantum Gravity,” Phys. Rev. D15
1977
Cited alongside, same era.
A. Uhlmann, “Relative Entropy and the Wigner-Yanase-Dyson-Lieb Concavity In An Interpolation Theory,” Commun. Math. Phys. 54
1977
Cited alongside, same era.
C. Holzhey, F. Larsen, and F. Wilczek, “Geometric and Renormalized Entropy in Conformal Field Theory,” Nucl. Phys. B424
1994
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D. Guido and R. Longo, “An Algebraic Spin and Statistics Theorem,” Commun. Math. Phys. 172
1995
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H.-J. Borchers, Translation Group and Particle Representations in Quantum Field Theory
1996
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H. Narnhofer and W. Thirring, “From Relative Entropy to Entropy,” Fizika 17
1998
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H. J. Borchers, “On Revolutionizing Quantum Field Theory With Tomita’s Modular Theory,” J. Math. Phys. 41
2000
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R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That
2000
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A. Strohmaier, R. Verch, and M. Wollenberg, “Microlocal Analysis of Quantum Fields in Curved Spacetimes: Analytic Wavefront Sets and Reeh-Schlieder Theorems,” J. Math. Phys. 43
2002
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M. A. Nielsen and D. Petz, “A Simple Proof of the Strong Subadditivity Inequality,” Quantum Information and Computation 5
2005
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H. Casini, “Relative Entropy And The Bekenstein Bound,” Class. Quant. Grav. 25
2008
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K. Sanders, “On The Reeh-Schlieder Property in Curved Spacetime,” Commun. Math. Phys. 288
2009
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H. Narnhofer and W. Thirring, “Entanglement, Bell Inequality, and All That,” J. Math. Phys. 52
2012
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A. Wall, “A Proof of the Generalized Second Law for Rapidly Changing Fields and Arbitrary Horizon Slices,” Phys. Rev. D85
2012
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K. Papadodiamas and S. Raju, “An Infalling Observer in AdS/CFT,” JHEP 1310
2013
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B. Simon, Operator Theory: A Comprehensive Course in Analysis, Part 4
2015
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J. Maldacena, S. H. Shenker, and D. Stanford, “A Bound On Chaos,” JHEP 1608
2016
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