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We review the discovery of reflection positivity.
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Julian Schwinger, Four-Dimensional Euclidean Formulation of Quantum Field Theory, 1958 Annual International Conference on High Energy Physics, at CERN
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by same author, On the Euclidean structure of relativistic field theory, Proceedings of the National Academy of Sciences
1958
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Kurt Symanzik, A Modified Model of Euclidean Quantum Field Theory, Courant Institute of Mathematical Sciences Report IMM-NYU 327, 132 pages, June 1964
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Res Jost, The General Theory of Quantized Fields
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by same author, Euclidean Quantum Field Theory. I. Equations for a Scalar Model, Journal of Mathematical Physics
1966
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Rudolf Haag, N.N. Hugenholtz, and M. Winnink, On the equilibrium states in quantum statistical mechanics, Comm. Math. Phys
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by same author, Euclidean Quantum Field Theory, in Local Quantum Theory
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Masamichi Takesaki, Tomita’s Theory of Modular Hilbert Algebras and Its Applications, Lecture Notes in Mathematics, Vol. 128. Springer-Verlag, Berlin, Heidelberg, and New York (1970)
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Roland Dobrushin and Robert Minlos, Construction of a One-Dimensional Quantum Field by Means of a Continuous Markov Field, Functional Analysis and Applications
1973
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Edward Nelson, Construction of Quantum Fields from Markoff Fields, J. Funct. Anal
1973
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by same author, The Free Markoff Field, J. Funct. Anal
1973
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by same author, Probability Theory and Euclidean Field Theory, in Constructive Quantum Field Theory. The 1973 “Ettore Majorana” International School of Mathematical Physics
1973
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Konrad Osterwalder, Euclidean Green’s Functions and Wightman Distributions, in Constructive Quantum Field Theory. The 1973 “Ettore Majorana” International School of Mathematical Physics
1973
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Konrad Osterwalder and Robert Schrader, Axioms for Euclidean Green’s Functions, Comm. Math. Phys
1973
Cited alongside, same era.
James Glimm, Arthur Jaffe, and Thomas Spencer, The Wightman Axioms and Particle Structure in the P ( ϕ ) 2 P(\phi)_{2} Quantum Field Model, Ann. of Math
1974
Cited alongside, same era.
Jürg Fröhlich, The Reconstruction of Quantum Fields from Euclidean Green’s Functions at Arbitrary Temperatures, Helv. Phys. Acta
1975
Cited alongside, same era.
by same author, Phase Transitions for φ 2 2 \varphi^{2}_{2} Quantum Fields, Commun. Math. Phys
1975
Cited alongside, same era.
by same author, Axioms for Euclidean Green’s functions II. Comm. Math. Phys
1975
Cited alongside, same era.
Marek Biskup, Reflection positivity and phase transitions in lattice spin models, arXiv:math-ph/0610025 , In:Methods of Contemporary Mathematical Statistical Physics, R. Kotecky (Editor), Lecture Notes in Mathematics
2009
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Stefano Chesi, Arthur Jaffe, Daniel Loss, and Fabio L. Pedrocchi, Vortex Loops and Majoranas, J. Math. Phys
2013
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Arthur Jaffe, Christian D. Jäkel, Roberto E. Martinez, II, Complex Classical Fields: a Framework for Reflection Positivity, Comm. Math. Phys
2014
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by same author, Complex classical fields: an example, J. Funct. Anal
2014
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Arthur Jaffe, Stochastic PDE, Reflection Positivity, and Quantum Fields, Journal of Statistical Physics
2015
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Jürg Fröhlich, Barry Simon, and Thomas Spencer, Infrared bounds, phase transitions and continuous symmetry breaking, Commun. Math. Phys
1976
Cited alongside, same era.
Abel Klein, Gaussian OS-positive processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete
1977
Cited alongside, same era.
Freeman Dyson, Elliott Lieb, and Barry Simon, Phase transitions in quantum spin systems with isotropic and nonisotropic interactions, J. Stat. Phys
1978
Cited alongside, same era.
Jürg Fröhlich, Robert Israel, Elliott Lieb, and Barry Simon, Phase Transitions and Reflection Positivity. I. General Theory and Long Range Lattice Models, Comm. Math. Phys
1978
Cited alongside, same era.
Konrad Osterwalder and Erhard Seiler, Gauge field theories on a lattice, Ann. Phys
1978
Cited alongside, same era.
James Glimm and Arthur Jaffe, A Note on Reflection Positivity, Lett. Math. Phys
1979
Cited alongside, same era.
Abel Klein and Larry Landau, Construction of a unique self-adjoint generator for a symmetric local semigroup. J. Funct. Anal
1981
Cited alongside, same era.
Arthur Jaffe, Fabio L. Pedrocchi, Reflection Positivity for Parafermions, Comm. Math. Phys
2015
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Michael Miller, The Origins of Schwinger’s Euclidean Green’s Functions, Studies in History and Philosophy of Modern Physics
2015
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Arthur Jaffe and Bas Janssens, Characterization of Reflection Positivity: Majoranas and Spins, Commun. Math. Phys
2016
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Chunlan Jiang, Zhengwei Liu, and Jinsong Wu, Noncommutative uncertainty principles, J. Funct. Anal
2016
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Palle Jorgensen, Karl-Hermann Neeb, and Gestur Ólafsson, Reflection Positive Stochastic Processes Indexed by Lie Groups, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
2016
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by same author, Reflection Positive Doubles, Jour. Funct, Anal
2017
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Arthur Jaffe and Zhengwei Liu, Planar Para Algebras and Reflection Positivity, Commun. Math. Phys
2017
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by same authorConstructive Simulation and Topological Design of Protocols, New Journal of Physics
2017
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Zhengwei Liu, Alex Wozniakowski, and Arthur Jaffe, Quon 3D Language for Quantum Information, PNAS
2017
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by same author, Mathematical Picture Language Program, PNAS
2018
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Arthur Jaffe, Zhengwei Liu, and Alex Wozniakowski, Holographic Software for Quantum Networks, SCIENCE CHINA Mathematics
2018
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