After graduating fromPelham Memorial High School in 1955,[3] Jaffe attendedPrinceton University as an undergraduate obtaining a degree in chemistry in 1959, and laterClare College, Cambridge, as aMarshall Scholar, obtaining a degree in mathematics in 1961. He then returned to Princeton, obtaining a doctorate in physics in 1966 withArthur Wightman. His whole career has been spent teaching mathematical physics and pursuing research atHarvard University. Jaffe was appointed as Professor of Physics in 1970, and had his title changed to Professor of Mathematical Physics in 1974. As part of this transition, Jaffe became a member of the mathematics department. He served as chair from 1987 to 1990.[4]
Jaffe conceived the idea of theClay Mathematics Institute and its programs, including the employment of research fellows and the Millennium Prizes in mathematics. He served as a founding member, a founding member of the board, and the founding president of that organization.
One of Arthur Jaffe's earliest contributions was his proof, joint with Henry Epstein andVladimir Glaser, that energy densities inlocal quantum field theories are always nonpositive.[6]
A large amount of Jaffe's work deals with the mathematical construction andproof of results in quantum field theory. Jaffe began his research on the topic in the late 1960s and early 1970s, at which point the only local quantum field theory which had been constructed mathematically was thefree field model. In a series of landmark papers, Jaffe and collaborators made great progress in understanding the nature of quantum field theory.[7][8][9][10][11][12] This culminated in the first ever mathematical local quantum field theory with non-linearity and non-trivial scattering.[13] Thus it established the mathematical compatibility ofspecial relativity,quantum theory, and interaction. For this work, Jaffe andJames Glimm are acknowledged as the founders of the subject ofconstructive quantum field theory.
Another notable contribution of Jaffe's is his proof, joint withJames Glimm andThomas Spencer, that quantum field theories can havephase transitions.[14][15] While physicists had conjectured for many years that this phenomenon took place, Jaffe-Glimm-Spencer's work gave the first mathematical proof. This work is also notable for using the formalism ofreflection positivity to establish its results, which has since become common practice among researchers studying phase transitions in quantum field theory.[16]
One recurring idea in Jaffe's works is the notion ofreflection positivity, which was first introduced by Osterwalder and Schrader while they were Jaffe's post-doctoral fellows. The notion of reflection positivity has served since its inception as a key tool in thequantization of classical Euclidean field theories into relativistic quantum field theories. It also provides a basic tool to study phase transitions both in statistical physics as well as in quantum field theory. Jaffe has made major contributions to the development of this theory, by establishing key examples,[17][18][19][20][21][22][23][24][25] introducing important generalizations,[26][27][28] and providing geometric interpretations.[29][30]
In his later years Arthur Jaffe has made varied contributions to the theory ofquantum information, along with postdoctoral researchers Zhengwei Liu, Kaifeng Bu, and students.[36][37][38][39] Notable among these contributions are the introduction of quantumFourier analysis,[40][41] the study of quantum resources,[42][43][44] quantum error correction,[45] and the introduction of a 3Dgraphical language for quantum information.[46]
Jaffe is the author of several essays on thephilosophy of mathematics andphysics, with a special emphasis on the role ofproof and rigor in these subjects.[47][48][49][50] The most influential of these works was his essay withFrank Quinn, which introduced the notion of "Theoretical Mathematics".[51] An issue of the Bulletin of theAmerican Mathematical Society was devoted to responses to this article, written by leading mathematicians.[52]
Arthur Jaffe is the recipient of numerous awards and honors. In 1979 he was awarded the New York Academy of Science prize in Mathematics and Physics.[53] In 1980 Arthur Jaffe was awarded theDannie Heineman Prize for Mathematical Physics. In 1990 he was awarded the Medal Collège de France.[54] In 2018 he was awarded theICCM prize for best mathematical paper in the last five years.[55] In 2020 he was awarded the Science China Mathematics Award for best editor.[53] Jaffe has been an invited speak at many distinguished conferences, including the 1978International Congress of Mathematicians atHelsinki.[56]
Jaffe was married from 1971 to 1992 to Nora Frances Crow, Ph.D., professor of English literature at Smith College. They had one daughter, Margaret Collins, born in 1986. Jaffe was married to artist Sarah Robbins Warren from 1992 to 2002.
^Cannon, John T.; Jaffe, Arthur M. (1 December 1970). "Lorentz covariance of the λ(ϕ4)2 quantum field theory".Communications in Mathematical Physics.17 (4):261–321.doi:10.1007/BF01646027.ISSN1432-0916.
^Jaffe, Arthur; Glimm, James (1973). "Positivity of the φ43 Hamiltonian".Fortschritte der Physik.21.
^Glimm, James; Jaffe, Arthur; Spencer, Thomas (1974). "The Wightman Axioms and Particle Structure in the P(φ)2 Quantum Field Model".Annals of Mathematics.100 (3):585–632.doi:10.2307/1970959.ISSN0003-486X.JSTOR1970959.
^Fröhlich, Jürg; Israel, Robert; Lieb, Elliot H.; Simon, Barry (1 August 1978). "Phase transitions and reflection positivity. I. General theory and long range lattice models".Communications in Mathematical Physics.62 (1):1–34.Bibcode:1978CMaPh..62....1F.doi:10.1007/BF01940327.ISSN1432-0916.
^Jaffe, Arthur; Klimek, Slawomir; Lesniewski, Andrzej (1 December 1989). "Representations of the Heisenberg algebra on a Riemann surface".Communications in Mathematical Physics.126 (2):421–431.Bibcode:1989CMaPh.126..421J.doi:10.1007/BF02125133.ISSN1432-0916.
^Jaffe, Arthur; Janssens, Bas (12 June 2015). "Characterization of Reflection Positivity: Majoranas and Spins".Communications in Mathematical Physics.346 (3):1021–1050.arXiv:1506.04197v2.doi:10.1007/s00220-015-2545-z.
^Jaffe, Arthur; Janssens, Bas (24 July 2016). "Reflection Positive Doubles".arXiv:1607.07126 [math-ph].
^Jaffe, Arthur; Jäkel, Christian D.; Martinez II, Roberto E. (29 January 2012). "Complex Classical Fields: A Framework for Reflection Positivity".arXiv:1201.6003v2 [math-ph].
^Jaffe, Arthur; Liu, Zhengwei (30 January 2019). "Reflection Positivity and Levin-Wen Models".arXiv:1901.10662v1 [math-ph].
^Jaffe, Arthur; Liu, Zhengwei (6 June 2020). "A Mathematical Picture Language Project".arXiv:2006.03954v1 [math-ph].
^Balaban, Tadeusz; Imbrie, John; Jaffe, Arthur (1985), Jaffe, Arthur; Lehmann, Harry; Mack, Gerhard (eds.), "Renormalization of the Higgs Model: Minimizers, Propagators and the Stability of Mean Field Theory",Quantum Field Theory: A Selection of Papers in Memoriam Kurt Symanzik, Berlin, Heidelberg: Springer, pp. 299–329,doi:10.1007/978-3-642-70307-2_17,hdl:2027.42/46529,ISBN978-3-642-70307-2{{citation}}: CS1 maint: work parameter with ISBN (link)
^Jaffe, Arthur; Liu, Zhengwei; Wozniakowski, Alex (1 May 2016). "Compressed Teleportation".arXiv:1605.00321v1 [quant-ph].
^Jaffe, Arthur; Liu, Zhengwei; Wozniakowski, Alex (19 November 2016). "Constructive simulation and topological design of protocols".New Journal of Physics.19 (6).arXiv:1611.06447v2.doi:10.1088/1367-2630/aa5b57.
^Jaffe, Arthur; Liu, Zhengwei; Wozniakowski, Alex (30 April 2016). "Holographic software for quantum networks".Science China Mathematics.61 (4):593–626.arXiv:1605.00127v5.doi:10.1007/s11425-017-9207-3.
^Jaffe, Arthur (2003). "The Role of Rigorous Proof in Modern Mathematical Thinking". In Hoff Kjeldsen, Tinne (ed.).New Trends in the History and Philosophy of Mathematics. University of Odense Press.
^Jaffe, Arthur (2003). "Interactions between Mathematics and Theoretical Physics". In Hoff Kjeldsen, Tinne (ed.).New Trends in the History and Philosophy of Mathematics. University of Odense Press.
^Jaffe, Arthur; Quinn, Frank (30 June 1993),Theoretical mathematics: Toward a cultural synthesis of mathematics and theoretical physics,arXiv:math/9307227,Bibcode:1993math......7227J
^Atiyah, Michael; Borel, Armand; Chaitin, G. J.; Friedan, Daniel; Glimm, James; Gray, Jeremy J.; Hirsch, Morris W.; MacLane, Saunder; Mandelbrot, Benoit B. (31 March 1994),Responses toTheoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics, by A. Jaffe and F. Quinn,arXiv:math/9404229,Bibcode:1994math......4229A
