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These notes provide an explanation of the type classification of von Neumann algebras, which has made many appearances in recent work on entanglement in quantum field theory and quantum gravity.
v. Neumann, J, Zur algebra der funktionaloperationen und theorie der normalen operatoren
1930
Earlier work this paper cites.
Murray, Francis J and Neumann, J v, On rings of operators
1936
Earlier work this paper cites.
Murray, Francis J and Von Neumann, John, On rings of operators. II
1937
Earlier work this paper cites.
Neumann, J v, On rings of operators. III
1940
Earlier work this paper cites.
Murray, Francis J and von Neumann, John, On rings of operators. IV
1943
Earlier work this paper cites.
Von Neumann, John, On rings of operators. Reduction theory
1949
Earlier work this paper cites.
Araki, Huzihiro and Woods, EJ, Representations of the canonical commutation relations describing a nonrelativistic infinite free Bose gas
1963
Earlier work this paper cites.
Araki, Huzihiro, Type of von Neumann algebra associated with free field
1964
Earlier work this paper cites.
A. Connes, Une classification des facteurs de type iii
1973
Earlier work this paper cites.
Rudin, Walter, Real and Complex Analysis, McGraw-Hill
1974
Earlier work this paper cites.
J. J. Bisognano and E. H. Wichmann, On the duality condition for a hermitian scalar field
1975
Earlier work this paper cites.
J. J. Bisognano and E. H. Wichmann, On the duality condition for quantum fields
1976
Earlier work this paper cites.
Driessler, W, On the type of local algebras in quantum field theory
1977
Earlier work this paper cites.
L.M.S. monographs. Academic Press, 1979
Pedersen, G.K., C*-algebras and Their Automorphism Groups · 1979
Earlier work this paper cites.
Gulf Professional Publishing, 1980
M. Reed, B. Simon, et al., I: Functional analysis · 1980
Cited alongside, same era.
Springer, 1985
Fredenhagen, Klaus, On the modular structure of local algebras of observables · 1985
Cited alongside, same era.
Buchholz, Detlev and D’Antoni, Claudio and Fredenhagen, Klaus, The universal structure of local algebras
1987
Cited alongside, same era.
International series in pure and applied mathematics. McGraw-Hill, 1991
Rudin, W., Functional Analysis · 1991
Cited alongside, same era.
Buchholz, Detlev and Verch, Rainer, Scaling algebras and renormalization group in algebraic quantum field theory
1995
Cited alongside, same era.
World Scientific Series In 20th Century Mathematics. World Scientific Publishing Company, 1995
Muraskin, M. and Brody, F. and Vamos, T., The Neumann Compendium · 1995
Springer Science & Business Media, 2012
Sunder, Viakalathur Shankar, An invitation to von Neumann algebras · 2012
Later among the works it cites.
Springer Science & Business Media, 2012
S. Sakai, C*-algebras and W*-algebras · 2012
Later among the works it cites.
Springer Science & Business Media, 2012
Haag, Rudolf, Local quantum physics: Fields, particles, algebras · 2012
Later among the works it cites.
D. Harlow, The Ryu-Takayanagi formula from quantum error correction
2017
Later among the works it cites.
Courier Dover Publications, 2017
J. L. Kelley, General topology · 2017
Later among the works it cites.
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Cited alongside, same era.
Springer Science & Business Media, 1998
Douglas, Ronald G, Banach algebra techniques in operator theory · 1998
Cited alongside, same era.
American Mathematical Soc., 2000
Conway, John B, A course in operator theory · 2000
Cited alongside, same era.
Encyclopaedia of Mathematical Sciences. Springer Berlin Heidelberg, 2001
Takesaki, M., Theory of Operator Algebras I · 2001
Cited alongside, same era.
Jones, Vaughan FR, von Neumann algebras
2003
Cited alongside, same era.
Springer, 2003
Takesaki, Masamichi and others, Theory of operator algebras II · 2003
Cited alongside, same era.
Yngvason, Jakob, The role of type III factors in quantum field theory
2005
Cited alongside, same era.
2018
Later among the works it cites.
2021
Later among the works it cites.
S. Leutheusser and H. Liu, Emergent times in holographic duality
2021
Later among the works it cites.
Witten, Edward, Gravity and the crossed product
2022
Later among the works it cites.
Witten, Edward, Why Does Quantum Field Theory In Curved Spacetime Make Sense? And What Happens To The Algebra of Observables In The Thermodynamic Limit? · 2022
Later among the works it cites.
Longo, Roberto and Witten, Edward, A note on continuous entropy
2022
Later among the works it cites.
2022
Later among the works it cites.
2022
Later among the works it cites.
Penington, Geoff and Witten, Edward, Algebras and States in JT Gravity
2023
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