33:
366:. In a series of landmark papers, Jaffe and collaborators made great progress in understanding the nature of quantum field theory. This culminated in the first ever mathematical local quantum field theory with non-linearity and non-trivial scattering. Thus it established the mathematical compatibility of
422:
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,
238:. 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.
2180:
Cain, Madelyn; Zhao, Chen; Zhou, Hengyun; Meister, Nadine; Ataides, J. Pablo
Bonilla; Jaffe, Arthur; Bluvstein, Dolev; Lukin, Mikhail D. (5 March 2024). "Correlated decoding of logical algorithms with transversal gates".
538:
prize for best mathematical paper in the last five years. In 2020 he was awarded the
Science China Mathematics Award for best editor. Jaffe has been an invited speak at many distinguished conferences, including the 1978
310:
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.
858:
361:
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 the
3344:
402:. 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 of
418:, 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 the
3309:
530:
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. In 1980 Arthur Jaffe was awarded the
1793:
590:
Jaffe was married from 1971 to 1992 to Nora
Frances Crow and they had one daughter, Margaret Collins, born in 1986. Jaffe was married to artist Sarah Robbins Warren from 1992 to 2002.
3274:
253:, Eugene Wayne, John Imbrie, Christopher King, and Jonathan Weitsman. In total, Jaffe has over 300 mathematical descendants. He has had many post-doctoral collaborators, including
3349:
2401:
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),
3319:
2552:
3324:
266:
567:
3339:
292:
535:
1550:
Jaffe, Arthur; Jäkel, Christian D.; Martinez II, Roberto E. (29 January 2012). "Complex
Classical Fields: A Framework for Reflection Positivity".
486:, along with postdoctoral researchers Zhengwei Liu, Kaifeng Bu, and students. Notable among these contributions are the introduction of quantum
837:"The $ \lambda(\varphi^4)_2$ quantum field theory without cutoffs. II. The field operators and the approximate vacuum | Annals of Mathematics"
531:
38:
3279:
3264:
3314:
406:
to establish its results, which has since become common practice among researchers studying phase transitions in quantum field theory.
3329:
607:
1860:
Jaffe, Arthur; Liu, Zhengwei; Wozniakowski, Alex (19 November 2016). "Constructive simulation and topological design of protocols".
2633:
540:
1934:
Li, Lu; Bu, Kaifeng; Koh, Dax Enshan; Jaffe, Arthur; Lloyd, Seth (12 August 2022). "Wasserstein
Complexity of Quantum Circuits".
395:
277:
316:
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1776:
1644:
571:
300:
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230:, obtaining a degree in mathematics in 1961. He then returned to Princeton, obtaining a doctorate in physics in 1966 with
3289:
2293:
551:
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2549:
379:
2024:
Bu, Kaifeng; Gu, Weichen; Jaffe, Arthur (16 February 2023). "Discrete
Quantum Gaussians and Central Limit Theorem".
2263:
Jaffe, Arthur (2003). "The Role of
Rigorous Proof in Modern Mathematical Thinking". In Hoff Kjeldsen, Tinne (ed.).
3094:
2278:
Jaffe, Arthur (2003). "Interactions between Mathematics and Theoretical Physics". In Hoff Kjeldsen, Tinne (ed.).
3185:
1897:
Jaffe, Arthur; Liu, Zhengwei; Wozniakowski, Alex (30 April 2016). "Holographic software for quantum networks".
1439:
Jaffe, Arthur; Janssens, Bas (12 June 2015). "Characterization of Reflection Positivity: Majoranas and Spins".
859:"The λ(φ4)2 quantum field theory without cutoffsquantum field theory without cutoffs: III. The physical vacuum"
647:
1394:
Chesi, Stefano; Jaffe, Arthur; Loss, Daniel; Pedrocchi, Fabio L. (27 May 2013). "Vortex loops and Majoranas".
3209:
2643:
2544:
1667:
563:
559:
519:
296:
3169:
2626:
2502:
1613:
Balaban, Tadeusz; Imbrie, John; Jaffe, Arthur (1985), Jaffe, Arthur; Lehmann, Harry; Mack, Gerhard (eds.),
575:
2066:
Chen, Liyuan; Garcia, Roy J.; Bu, Kaifeng; Jaffe, Arthur (2024). "Magic of random matrix product states".
463:. The JLO construction takes as input a supersymmetric quantum field theory (mathematically, a θ-summable
515:
325:
215:
3299:
2896:
307:
2563:"School of Theoretical Physics Statutory Public Lecture "Beauty and Truth in Mathematics and Physics""
1235:
Jaffe, Arthur; Pedrocchi, Fabio L. (1 February 2014). "Topological Order and Reflection Positivity".
555:
503:
1615:"Renormalization of the Higgs Model: Minimizers, Propagators and the Stability of Mean Field Theory"
299:. He chaired the Council of Scientific Society Presidents. He served as chair of the board of the
223:
82:
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665:
633:
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2690:
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2619:
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in 1979 and served for 21 years until 2001. He served as distinguished visiting professor at the
2045:
Bu, Kaifeng; Gu, Weichen; Jaffe, Arthur (15 June 2023). "Stabilizer Testing and Magic Entropy".
3304:
2773:
419:
191:
1571:
Jaffe, Arthur; Liu, Zhengwei (30 January 2019). "Reflection Positivity and Levin-Wen Models".
1002:"Phase transitions and reflection positivity. I. General theory and long range lattice models"
679:
2995:
2987:
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2832:
2816:
2757:
1955:
Jaffe, Arthur; Jiang, Chunlan; Liu, Zhengwei; Ren, Yunxiang; Wu, Jinsong (10 February 2020).
1756:
507:
342:
271:
518:, which introduced the notion of "Theoretical Mathematics". An issue of the Bulletin of the
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2420:
2405:
Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics
2384:
2134:
2085:
1978:
1839:
Jaffe, Arthur; Liu, Zhengwei; Wozniakowski, Alex (1 May 2016). "Compressed Teleportation".
1805:
1763:. Lecture Notes in Physics. Vol. 370. Berlin, Heidelberg: Springer. pp. 375–397.
1721:
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1516:
1413:
1360:
1307:
1254:
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1013:
768:"A $ \ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ Quantum Field Theory without Cutoffs. I"
717:
346:
219:
99:
78:
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611:
234:. His whole career has been spent teaching mathematical physics and pursuing research at
8:
2840:
2749:
2725:
2674:
579:
490:, the study of quantum resources, quantum error correction, and the introduction of a 3D
483:
341:
One of Arthur Jaffe's earliest contributions was his proof, joint with Henry Epstein and
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2157:
2138:
2112:
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1982:
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2410:
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2240:
2215:
2203:
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2075:
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2025:
2001:
1968:
1956:
1935:
1906:
1869:
1840:
1593:
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Jaffe, Arthur; Liu, Zhengwei (6 June 2020). "A Mathematical Picture Language Project".
1572:
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1506:
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1403:
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944:
511:
460:
415:
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367:
358:
285:
258:
235:
195:
109:
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Jaffe, Arthur; Ritter, Gordon (1 May 2008). "Reflection Positivity and Monotonicity".
3062:
3019:
2963:
2888:
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2245:
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2006:
1821:
1772:
1737:
1733:
1640:
1532:
1376:
1341:
Jaffe, Arthur; Pedrocchi, Fabio L. (2015). "Reflection Positivity for Parafermions".
1323:
1270:
1217:
1176:
1123:
1076:
1029:
963:
936:
878:
818:
733:
436:
371:
288:, Tadeusz Balaban, Andrew Lesniewski, Slawomir Klimek, Zhengwei Liu, and Kaifeng Bu.
1497:
Jaffe, Arthur; Liu, Zhengwei (2017). "Planar Para Algebras, Reflection Positivity".
1266:
767:
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and rigor in these subjects. The most influential of these works was his essay with
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1996:
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1207:
1168:
1115:
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1021:
928:
870:
810:
779:
725:
487:
399:
227:
167:
116:
2741:
1288:
Jaffe, Arthur; Pedrocchi, Fabio L. (2015). "Reflection Positivity for Majoranas".
836:
32:
3011:
2912:
2556:
1708:
Balaban, Tadeusz; Imbrie, John; Jaffe, Arthur; Brydges, David (1 December 1984).
1626:
534:. In 1990 he was awarded the Medal Collège de France. In 2018 he was awarded the
471:
464:
432:
281:
262:
254:
250:
231:
139:
121:
2097:
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introducing important generalizations, and providing geometric interpretations.
3161:
3070:
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2955:
2460:
1883:
1614:
1000:
Fröhlich, Jürg; Israel, Robert; Lieb, Elliot H.; Simon, Barry (1 August 1978).
491:
482:
In his later years Arthur Jaffe has made varied contributions to the theory of
203:
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2579:
2562:
2336:
1920:
1528:
1462:
1372:
1319:
1212:
1195:
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Additionally, Jaffe is a fellow of many mathematical societies, including the
3258:
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3110:
3102:
3086:
3003:
2880:
2824:
2797:
2682:
2344:
1825:
1768:
1741:
1536:
1380:
1327:
1274:
1221:
1180:
1127:
1080:
1033:
940:
917:"The Wightman Axioms and Particle Structure in the P(φ)2 Quantum Field Model"
882:
822:
783:
737:
522:
was devoted to responses to this article, written by leading mathematicians.
452:
440:
199:
68:
2540:
2230:
2147:
1991:
1476:
Jaffe, Arthur; Janssens, Bas (24 July 2016). "Reflection Positive Doubles".
1194:
Jaffe, Arthur; Jäkel, Christian D.; Martinez, Roberto E. (1 February 2014).
357:
A large amount of Jaffe's work deals with the mathematical construction and
3233:
2781:
2717:
2503:"ICM Plenary and Invited Speakers | International Mathematical Union (IMU)"
2249:
2166:
2010:
751:
Jaffe, Arthur (1966). "Existence Theorems for a Cut-off λφ4 Field Theory".
468:
246:
242:
135:
131:
3225:
3201:
3177:
3038:
2904:
2709:
2486:"2018 annual meeting of International Congress of Chinese Mathematicians"
1635:
982:
896:
Jaffe, Arthur; Glimm, James (1973). "Positivity of the φ43 Hamiltonian".
456:
391:
375:
145:
2352:
2320:
1094:
Jaffe, Arthur; Klimek, Slawomir; Lesniewski, Andrzej (1 December 1989).
3153:
3046:
1817:
1694:
1119:
1072:
1025:
948:
916:
874:
814:
729:
648:"Oral History Interviews. Arthur Jaffe, interviewed by Katherine Sopka"
363:
222:
as an undergraduate obtaining a degree in chemistry in 1959, and later
2535:
1425:
1172:
3241:
3217:
3054:
2415:
2379:
2220:
2129:
2080:
2051:
2030:
1973:
1940:
1911:
1874:
1845:
1619:
Quantum Field Theory: A Selection of Papers in Memoriam Kurt Symanzik
1598:
1577:
1453:
1095:
1048:
1001:
798:
705:
2371:: Toward a cultural synthesis of mathematics and theoretical physics
2202:
Liu, Zhengwei; Wozniakowski, Alex; Jaffe, Arthur (8 December 2016).
1668:"Effective Action and Cluster Properties of the Abelian Higgs Model"
1556:
1408:
932:
3345:
Presidents of the International Association of Mathematical Physics
2641:
2187:
1511:
1482:
544:
431:
Jaffe is also known for his mathematical proof of an aspect of the
1355:
1302:
1249:
1155:
706:"Nonpositivity of the energy density in quantized field theories"
390:
Another notable contribution of Jaffe's is his proof, joint with
1792:
Jaffe, Arthur; Lesniewski, Andrzej; Osterwalder, Konrad (1988).
1096:"Representations of the Heisenberg algebra on a Riemann surface"
2580:"Arthur Jaffe | Is relativity compatible with quantum theory?"
2575:(lecture by Arthur Jaffe, 18 May 2016, Trinity College Dublin)
2530:
3310:
Fellows of the Society for Industrial and Applied Mathematics
2598:. IMBM Istanbul Matematiksel Bilimler Merkezi. 20 June 2021.
321:
385:
2536:
Mathematical Picture Language Project at Harvard University
182:
1791:
173:
3275:
Members of the United States National Academy of Sciences
2400:
1707:
666:"Harvard University list of Faculty of Arts and Sciences"
634:"Harvard University list of Faculty of Arts and Sciences"
176:
497:
2461:"Arthur M. Jaffe – Hagler Institute for Advanced Study"
2280:
New Trends in the History and Philosophy of Mathematics
2265:
New Trends in the History and Philosophy of Mathematics
1393:
999:
983:"Existence of Phase Transitions for φ42 Quantum Fields"
799:"Lorentz covariance of the λ(ϕ4)2 quantum field theory"
3350:
Academics of the Dublin Institute for Advanced Studies
1666:
Jaffe, Arthur; Imbrie, John; Balaban, Tadeusz (1988).
2550:
Dublin Institute for Advanced Study: Governing Boards
1549:
1093:
981:
Jaffe, Arthur; Glimm, James; Spencer, Thomas (1976).
962:
Jaffe, Arthur; Glimm, James; Thomas, Spencer (1975).
915:
Glimm, James; Jaffe, Arthur; Spencer, Thomas (1974).
797:
Cannon, John T.; Jaffe, Arthur M. (1 December 1970).
414:
One recurring idea in Jaffe's works is the notion of
179:
2201:
1896:
1859:
1838:
352:
303:, School of Theoretical Physics, from 2005 to 2020.
2179:
2111:Garcia, Roy J.; Bu, Kaifeng; Jaffe, Arthur (2023).
704:Epstein, H.; Glaser, V.; Jaffe, A. (1 April 1965).
568:
American Association for the Advancement of Science
378:are acknowledged as the founders of the subject of
170:
1665:
1621:, Berlin, Heidelberg: Springer, pp. 299–329,
1612:
1193:
703:
459:, along with collaborators Andrzej Lesniewski and
336:
206:Professor of Mathematics and Theoretical Science.
2065:
1757:"KMS states, cyclic cohomology and supersymmetry"
1710:"The mass gap for Higgs models on a unit lattice"
980:
914:
293:International Association of Mathematical Physics
3256:
2607:List of Past AMS Presidents (Jaffe is the 54th.)
2592:"Arthur Jaffe (Harvard): Remembering the Future"
1954:
1047:Glimm, James; Jaffe, Arthur (1 September 1979).
961:
766:Glimm, James; Jaffe, Arthur (25 December 1968).
560:Society of Industrial and Applied Mathematicians
439:in the abelian Higgs model induces a gap in the
3320:Presidents of the American Mathematical Society
2208:Proceedings of the National Academy of Sciences
2117:Proceedings of the National Academy of Sciences
1961:Proceedings of the National Academy of Sciences
1794:"Quantum $ K$ -theory. I. The Chern character"
1340:
1287:
1234:
532:Dannie Heineman Prize for Mathematical Physics
2627:
2110:
1759:. In Doebner, H. -D.; Hennig, J. -D. (eds.).
1475:
1438:
502:Jaffe is the author of several essays on the
291:For several years Jaffe was president of the
241:Arthur Jaffe's 30 doctoral students include
3325:Fellows of the American Mathematical Society
2366:Jaffe, Arthur; Quinn, Frank (30 June 1993),
1933:
987:Mathematical Methods of Quantum Field Theory
374:, and interaction. For this work, Jaffe and
1140:
796:
753:Mathematical Theory of Elementary Particles
2634:
2620:
2365:
2204:"Quon 3D language for quantum information"
1046:
964:"Phase Transitions for φ42 Quantum Fields"
895:
856:
765:
322:Academy of Mathematics and Systems Science
2414:
2378:
2239:
2229:
2219:
2186:
2156:
2146:
2128:
2079:
2050:
2044:
2029:
2023:
2000:
1990:
1972:
1939:
1910:
1873:
1844:
1634:
1597:
1576:
1555:
1510:
1481:
1452:
1407:
1354:
1301:
1248:
1211:
1154:
510:, with a special emphasis on the role of
386:Phase Transitions in Quantum Field Theory
190:; born December 22, 1937) is an American
3340:Fellows of the American Physical Society
2321:"Proof and the Evolution of Mathematics"
1591:
1570:
1496:
541:International Congress of Mathematicians
455:Jaffe is most known for introducing the
446:
409:
2113:"Resource theory of quantum scrambling"
1754:
398:, that quantum field theories can have
209:
3257:
2602:from the original on 19 December 2021.
2573:from the original on 19 December 2021.
1798:Communications in Mathematical Physics
1675:Communications in Mathematical Physics
1499:Communications in Mathematical Physics
1441:Communications in Mathematical Physics
1343:Communications in Mathematical Physics
1196:"Complex classical fields: An example"
1100:Communications in Mathematical Physics
1006:Communications in Mathematical Physics
968:Communications in Mathematical Physics
803:Communications in Mathematical Physics
477:
317:Communications in Mathematical Physics
314:Arthur Jaffe began as chief editor of
2615:
2441:
2437:
2435:
2433:
2318:
2277:
2262:
750:
572:American Academy of Arts and Sciences
498:Philosophy of Mathematics and Physics
453:supersymmetric quantum field theories
301:Dublin Institute for Advanced Studies
3280:21st-century American mathematicians
3265:20th-century American mathematicians
857:Glimm, James; Jaffe, Arthur (1970).
525:
552:Hagler Institute for Advanced Study
13:
3315:Members of the Royal Irish Academy
2430:
14:
3361:
2569:. Oracle Pictures. 14 June 2016.
2524:
1049:"A note on reflection positivity"
626:
380:constructive quantum field theory
353:Constructive Quantum Field Theory
3330:American mathematical physicists
2586:. Harvard CMSA. 2 December 2020.
585:
578:, and an honorary member of the
306:Jaffe conceived the idea of the
166:
31:
2495:
2478:
2453:
2394:
2359:
2312:
2294:"Equations for universal truth"
2286:
2271:
2256:
2195:
2173:
2104:
2059:
2038:
2017:
1948:
1927:
1890:
1853:
1832:
1785:
1748:
1701:
1659:
1606:
1585:
1564:
1543:
1490:
1469:
1432:
1396:Journal of Mathematical Physics
1387:
1334:
1281:
1228:
1187:
1143:Journal of Mathematical Physics
1134:
1087:
1053:Letters in Mathematical Physics
1040:
993:
974:
955:
908:
889:
850:
829:
576:US National Academy of Sciences
426:
337:Nonpositivity of Energy Density
1200:Journal of Functional Analysis
790:
759:
744:
697:
672:
658:
640:
600:
1:
2644:American Mathematical Society
2545:Mathematics Genealogy Project
2282:. University of Odense Press.
2267:. University of Odense Press.
652:American Institute of Physics
593:
564:American Mathematical Society
520:American Mathematical Society
297:American Mathematical Society
198:, where in 1985 he succeeded
2298:Times Higher Education (THE)
1734:10.1016/0003-4916(84)90121-0
1627:10.1007/978-3-642-70307-2_17
710:Il Nuovo Cimento (1955-1965)
347:local quantum field theories
7:
3295:Princeton University alumni
3285:American quantum physicists
2098:10.1103/PhysRevB.109.174207
1267:10.1209/0295-5075/105/40002
467:) and outputs a cocycle in
345:, that energy densities in
331:
326:Chinese Academy of Sciences
216:Pelham Memorial High School
10:
3366:
3290:Harvard University faculty
2897:Theophil Henry Hildebrandt
2407:, by A. Jaffe and F. Quinn
1957:"Quantum Fourier analysis"
308:Clay Mathematics Institute
3335:Santa Fe Institute people
3145:
3030:
2923:
2808:
2701:
2650:
1921:10.1007/s11425-017-9207-3
1899:Science China Mathematics
1529:10.1007/s00220-016-2779-4
1463:10.1007/s00220-015-2545-z
1373:10.1007/s00220-015-2340-x
1320:10.1007/s00023-014-0311-y
1237:EPL (Europhysics Letters)
1213:10.1016/j.jfa.2013.08.033
684:www.sciencepresidents.org
556:American Physical Society
504:philosophy of mathematics
494:for quantum information.
435:. Namely, he showed that
155:
127:
115:
105:
95:
88:
74:
64:
46:
30:
23:
1884:10.1088/1367-2630/aa5b57
1769:10.1007/3-540-53503-9_55
784:10.1103/PhysRev.176.1945
570:. He is a member of the
349:are always nonpositive.
224:Clare College, Cambridge
218:in 1955, Jaffe attended
83:Clare College, Cambridge
3119:Cathleen Synge Morawetz
2691:Robert Simpson Woodward
2659:John Howard Van Amringe
2555:5 November 2020 at the
2369:Theoretical mathematics
2337:10.1023/A:1004903010713
2231:10.1073/pnas.1621345114
2148:10.1073/pnas.2217031120
1992:10.1073/pnas.2002813117
898:Fortschritte der Physik
433:abelian Higgs mechanism
2774:Leonard Eugene Dickson
2442:Jaffe, Arthur (2021).
2319:Jaffe, Arthur (1997).
1862:New Journal of Physics
1290:Annales Henri Poincaré
755:– via MIT Press.
214:After graduating from
192:mathematical physicist
16:American mathematician
2996:Charles B. Morrey Jr.
2988:Abraham Adrian Albert
2940:Gordon Thomas Whyburn
2833:Earle Raymond Hedrick
2817:George David Birkhoff
2758:Edward Burr Van Vleck
921:Annals of Mathematics
447:Supersymmetric Models
416:reflection positivity
410:Reflection Positivity
404:reflection positivity
2948:Raymond Louis Wilder
2766:Ernest William Brown
1755:Kastler, D. (1990).
680:"CSSP Board History"
220:Princeton University
210:Education and career
162:Arthur Michael Jaffe
100:Mathematical physics
79:Princeton University
2841:Luther P. Eisenhart
2750:Henry Burchard Fine
2726:William Fogg Osgood
2675:George William Hill
2444:"Arthur Jaffe's CV"
2425:1994math......4229A
2389:1993math......7227J
2139:2023PNAS..12017031G
2123:(17): e2217031120.
2090:2024PhRvB.109q4207C
1983:2020PNAS..11710715J
1967:(20): 10715–10720.
1810:1988CMaPh.118....1J
1726:1984AnPhy.158..281B
1687:1988CMaPh.114..257B
1521:2017CMaPh.352...95J
1418:2013JMP....54k2203C
1365:2015CMaPh.337..455J
1312:2015AnHP...16..189J
1259:2014EL....10540002J
1165:2008JMP....49e2301J
1112:1989CMaPh.126..421J
1065:1979LMaPh...3..377G
1018:1978CMaPh..62....1F
722:1965NCim...36.1016E
654:. 15 February 1977.
580:Royal Irish Academy
484:quantum information
478:Quantum Information
451:Within his work on
295:, and later of the
2849:Arthur Byron Coble
2790:Gilbert Ames Bliss
2642:Presidents of the
1818:10.1007/BF01218474
1695:10.1007/BF01225038
1120:10.1007/BF02125133
1073:10.1007/BF00397210
1026:10.1007/BF01940327
875:10.1007/BF02392335
815:10.1007/BF01646027
730:10.1007/BF02749799
492:graphical language
461:Konrad Osterwalder
368:special relativity
286:Krzysztof Gawedzki
259:Konrad Osterwalder
236:Harvard University
196:Harvard University
110:Harvard University
3300:Marshall Scholars
3252:
3251:
3063:Andrew M. Gleason
3020:Saunders Mac Lane
2964:Edward J. McShane
2889:Marshall H. Stone
2873:Griffith C. Evans
2857:Solomon Lefschetz
2734:Henry Seely White
2507:www.mathunion.org
2214:(10): 2497–2502.
2068:Physical Review B
1778:978-3-540-46647-5
1714:Annals of Physics
1646:978-3-642-70307-2
1426:10.1063/1.4829273
1173:10.1063/1.2907660
989:– via CNRS.
869:(none): 203–267.
608:"Website of ACAP"
526:Awards and honors
472:cyclic cohomology
437:symmetry breaking
400:phase transitions
159:
158:
151:Jonathan Weitsman
149:Christopher King
128:Doctoral students
90:Scientific career
57:December 22, 1937
3357:
3245:
3237:
3229:
3221:
3213:
3205:
3197:
3194:Eric Friedlander
3189:
3181:
3173:
3165:
3157:
3138:
3130:
3122:
3114:
3106:
3098:
3090:
3082:
3079:Irving Kaplansky
3074:
3066:
3058:
3050:
3042:
3023:
3015:
3007:
2999:
2991:
2983:
2975:
2972:Deane Montgomery
2967:
2959:
2951:
2943:
2935:
2932:John von Neumann
2916:
2908:
2900:
2892:
2884:
2876:
2868:
2865:Robert Lee Moore
2860:
2852:
2844:
2836:
2828:
2820:
2801:
2793:
2785:
2777:
2769:
2761:
2753:
2745:
2737:
2729:
2721:
2713:
2694:
2686:
2678:
2670:
2667:Emory McClintock
2662:
2636:
2629:
2622:
2613:
2612:
2603:
2587:
2574:
2518:
2517:
2515:
2513:
2499:
2493:
2492:
2490:
2482:
2476:
2475:
2473:
2471:
2457:
2451:
2450:
2448:
2439:
2428:
2427:
2418:
2398:
2392:
2391:
2382:
2363:
2357:
2356:
2316:
2310:
2309:
2307:
2305:
2290:
2284:
2283:
2275:
2269:
2268:
2260:
2254:
2253:
2243:
2233:
2223:
2199:
2193:
2192:
2190:
2177:
2171:
2170:
2160:
2150:
2132:
2108:
2102:
2101:
2083:
2063:
2057:
2056:
2054:
2042:
2036:
2035:
2033:
2021:
2015:
2014:
2004:
1994:
1976:
1952:
1946:
1945:
1943:
1931:
1925:
1924:
1914:
1894:
1888:
1887:
1877:
1857:
1851:
1850:
1848:
1836:
1830:
1829:
1789:
1783:
1782:
1752:
1746:
1745:
1705:
1699:
1698:
1672:
1663:
1657:
1656:
1655:
1653:
1638:
1610:
1604:
1603:
1601:
1589:
1583:
1582:
1580:
1568:
1562:
1561:
1559:
1547:
1541:
1540:
1514:
1494:
1488:
1487:
1485:
1473:
1467:
1466:
1456:
1447:(3): 1021–1050.
1436:
1430:
1429:
1411:
1391:
1385:
1384:
1358:
1338:
1332:
1331:
1305:
1285:
1279:
1278:
1252:
1232:
1226:
1225:
1215:
1206:(3): 1833–1881.
1191:
1185:
1184:
1158:
1138:
1132:
1131:
1091:
1085:
1084:
1044:
1038:
1037:
997:
991:
990:
978:
972:
971:
959:
953:
952:
912:
906:
905:
893:
887:
886:
863:Acta Mathematica
854:
848:
847:
845:
843:
833:
827:
826:
794:
788:
787:
778:(5): 1945–1951.
763:
757:
756:
748:
742:
741:
716:(3): 1016–1022.
701:
695:
694:
692:
690:
676:
670:
669:
662:
656:
655:
644:
638:
637:
630:
624:
623:
621:
619:
610:. Archived from
604:
488:Fourier analysis
364:free field model
275:
228:Marshall Scholar
189:
188:
185:
184:
181:
178:
175:
172:
117:Doctoral advisor
60:
56:
54:
35:
21:
20:
3365:
3364:
3360:
3359:
3358:
3356:
3355:
3354:
3255:
3254:
3253:
3248:
3240:
3232:
3224:
3216:
3208:
3200:
3192:
3184:
3176:
3168:
3160:
3152:
3141:
3133:
3125:
3117:
3109:
3101:
3095:William Browder
3093:
3085:
3077:
3069:
3061:
3053:
3045:
3037:
3026:
3018:
3012:Nathan Jacobson
3010:
3002:
2994:
2986:
2978:
2970:
2962:
2954:
2946:
2938:
2930:
2919:
2913:Joseph L. Walsh
2911:
2903:
2895:
2887:
2879:
2871:
2863:
2855:
2847:
2839:
2831:
2823:
2815:
2804:
2796:
2788:
2780:
2772:
2764:
2756:
2748:
2740:
2732:
2724:
2716:
2708:
2697:
2689:
2681:
2673:
2665:
2657:
2646:
2640:
2590:
2578:
2561:
2557:Wayback Machine
2531:Jaffe's website
2527:
2522:
2521:
2511:
2509:
2501:
2500:
2496:
2488:
2484:
2483:
2479:
2469:
2467:
2459:
2458:
2454:
2446:
2440:
2431:
2399:
2395:
2364:
2360:
2317:
2313:
2303:
2301:
2292:
2291:
2287:
2276:
2272:
2261:
2257:
2200:
2196:
2178:
2174:
2109:
2105:
2064:
2060:
2043:
2039:
2022:
2018:
1953:
1949:
1932:
1928:
1895:
1891:
1858:
1854:
1837:
1833:
1790:
1786:
1779:
1753:
1749:
1706:
1702:
1670:
1664:
1660:
1651:
1649:
1647:
1611:
1607:
1590:
1586:
1569:
1565:
1548:
1544:
1495:
1491:
1474:
1470:
1437:
1433:
1392:
1388:
1339:
1335:
1286:
1282:
1233:
1229:
1192:
1188:
1139:
1135:
1092:
1088:
1045:
1041:
998:
994:
979:
975:
960:
956:
933:10.2307/1970959
913:
909:
894:
890:
855:
851:
841:
839:
835:
834:
830:
795:
791:
772:Physical Review
764:
760:
749:
745:
702:
698:
688:
686:
678:
677:
673:
664:
663:
659:
646:
645:
641:
632:
631:
627:
617:
615:
614:on 13 July 2019
606:
605:
601:
596:
588:
528:
500:
480:
465:spectral triple
449:
429:
412:
388:
355:
343:Vladimir Glaser
339:
334:
282:Antti Kupiainen
269:
263:Juerg Froehlich
255:Robert Schrader
251:Clifford Taubes
232:Arthur Wightman
212:
169:
165:
150:
148:
144:
142:
140:Clifford Taubes
138:
134:
122:Arthur Wightman
81:
75:Alma mater
58:
52:
50:
42:
26:
25:Arthur M. Jaffe
17:
12:
11:
5:
3363:
3353:
3352:
3347:
3342:
3337:
3332:
3327:
3322:
3317:
3312:
3307:
3302:
3297:
3292:
3287:
3282:
3277:
3272:
3267:
3250:
3249:
3247:
3246:
3238:
3230:
3222:
3214:
3206:
3198:
3190:
3186:George Andrews
3182:
3174:
3166:
3162:David Eisenbud
3158:
3149:
3147:
3143:
3142:
3140:
3139:
3131:
3123:
3115:
3107:
3099:
3091:
3083:
3075:
3071:Julia Robinson
3067:
3059:
3051:
3043:
3034:
3032:
3028:
3027:
3025:
3024:
3016:
3008:
3000:
2992:
2984:
2980:Joseph L. Doob
2976:
2968:
2960:
2956:Richard Brauer
2952:
2944:
2936:
2927:
2925:
2921:
2920:
2918:
2917:
2909:
2901:
2893:
2885:
2877:
2869:
2861:
2853:
2845:
2837:
2829:
2821:
2812:
2810:
2806:
2805:
2803:
2802:
2794:
2786:
2778:
2770:
2762:
2754:
2746:
2738:
2730:
2722:
2714:
2705:
2703:
2699:
2698:
2696:
2695:
2687:
2679:
2671:
2663:
2654:
2652:
2648:
2647:
2639:
2638:
2631:
2624:
2616:
2610:
2609:
2604:
2588:
2576:
2559:
2547:
2538:
2533:
2526:
2525:External links
2523:
2520:
2519:
2494:
2477:
2452:
2429:
2393:
2358:
2331:(2): 133–146.
2311:
2300:. 28 July 2000
2285:
2270:
2255:
2194:
2172:
2103:
2074:(17): 174207.
2058:
2037:
2016:
1947:
1926:
1905:(4): 593–626.
1889:
1852:
1831:
1784:
1777:
1761:Quantum Groups
1747:
1720:(2): 281–319.
1700:
1681:(2): 257–315.
1658:
1645:
1605:
1584:
1563:
1542:
1489:
1468:
1431:
1386:
1349:(1): 455–472.
1333:
1296:(1): 189–203.
1280:
1227:
1186:
1133:
1106:(2): 421–431.
1086:
1059:(5): 377–378.
1039:
992:
973:
970:(45): 203–216.
954:
927:(3): 585–632.
907:
888:
849:
828:
809:(4): 261–321.
789:
758:
743:
696:
671:
657:
639:
625:
598:
597:
595:
592:
587:
584:
527:
524:
499:
496:
479:
476:
448:
445:
428:
425:
411:
408:
396:Thomas Spencer
387:
384:
372:quantum theory
354:
351:
338:
335:
333:
330:
278:Thomas Spencer
211:
208:
204:Landon T. Clay
157:
156:
153:
152:
129:
125:
124:
119:
113:
112:
107:
103:
102:
97:
93:
92:
86:
85:
76:
72:
71:
66:
62:
61:
48:
44:
43:
36:
28:
27:
24:
15:
9:
6:
4:
3:
2:
3362:
3351:
3348:
3346:
3343:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3316:
3313:
3311:
3308:
3306:
3305:Living people
3303:
3301:
3298:
3296:
3293:
3291:
3288:
3286:
3283:
3281:
3278:
3276:
3273:
3271:
3268:
3266:
3263:
3262:
3260:
3243:
3239:
3235:
3231:
3227:
3223:
3219:
3215:
3211:
3210:Robert Bryant
3207:
3203:
3199:
3195:
3191:
3187:
3183:
3179:
3175:
3171:
3167:
3163:
3159:
3155:
3151:
3150:
3148:
3144:
3136:
3135:Felix Browder
3132:
3128:
3124:
3120:
3116:
3112:
3111:Ronald Graham
3108:
3104:
3103:Michael Artin
3100:
3096:
3092:
3088:
3087:George Mostow
3084:
3080:
3076:
3072:
3068:
3064:
3060:
3056:
3052:
3048:
3044:
3040:
3036:
3035:
3033:
3029:
3021:
3017:
3013:
3009:
3005:
3004:Oscar Zariski
3001:
2997:
2993:
2989:
2985:
2981:
2977:
2973:
2969:
2965:
2961:
2957:
2953:
2949:
2945:
2941:
2937:
2933:
2929:
2928:
2926:
2922:
2914:
2910:
2906:
2902:
2898:
2894:
2890:
2886:
2882:
2881:Marston Morse
2878:
2874:
2870:
2866:
2862:
2858:
2854:
2850:
2846:
2842:
2838:
2834:
2830:
2826:
2825:Virgil Snyder
2822:
2818:
2814:
2813:
2811:
2807:
2799:
2798:Oswald Veblen
2795:
2791:
2787:
2783:
2779:
2775:
2771:
2767:
2763:
2759:
2755:
2751:
2747:
2743:
2742:Maxime Bôcher
2739:
2735:
2731:
2727:
2723:
2719:
2715:
2711:
2707:
2706:
2704:
2700:
2692:
2688:
2684:
2683:Simon Newcomb
2680:
2676:
2672:
2668:
2664:
2660:
2656:
2655:
2653:
2649:
2645:
2637:
2632:
2630:
2625:
2623:
2618:
2617:
2614:
2608:
2605:
2601:
2597:
2593:
2589:
2585:
2581:
2577:
2572:
2568:
2564:
2560:
2558:
2554:
2551:
2548:
2546:
2542:
2539:
2537:
2534:
2532:
2529:
2528:
2508:
2504:
2498:
2487:
2481:
2466:
2465:hias.tamu.edu
2462:
2456:
2445:
2438:
2436:
2434:
2426:
2422:
2417:
2412:
2408:
2404:
2403:Responses to
2397:
2390:
2386:
2381:
2376:
2372:
2368:
2362:
2354:
2350:
2346:
2342:
2338:
2334:
2330:
2326:
2322:
2315:
2299:
2295:
2289:
2281:
2274:
2266:
2259:
2251:
2247:
2242:
2237:
2232:
2227:
2222:
2217:
2213:
2209:
2205:
2198:
2189:
2184:
2176:
2168:
2164:
2159:
2154:
2149:
2144:
2140:
2136:
2131:
2126:
2122:
2118:
2114:
2107:
2099:
2095:
2091:
2087:
2082:
2077:
2073:
2069:
2062:
2053:
2048:
2041:
2032:
2027:
2020:
2012:
2008:
2003:
1998:
1993:
1988:
1984:
1980:
1975:
1970:
1966:
1962:
1958:
1951:
1942:
1937:
1930:
1922:
1918:
1913:
1908:
1904:
1900:
1893:
1885:
1881:
1876:
1871:
1867:
1863:
1856:
1847:
1842:
1835:
1827:
1823:
1819:
1815:
1811:
1807:
1803:
1799:
1795:
1788:
1780:
1774:
1770:
1766:
1762:
1758:
1751:
1743:
1739:
1735:
1731:
1727:
1723:
1719:
1715:
1711:
1704:
1696:
1692:
1688:
1684:
1680:
1676:
1669:
1662:
1648:
1642:
1637:
1636:2027.42/46529
1632:
1628:
1624:
1620:
1616:
1609:
1600:
1595:
1588:
1579:
1574:
1567:
1558:
1553:
1546:
1538:
1534:
1530:
1526:
1522:
1518:
1513:
1508:
1505:(1): 95–133.
1504:
1500:
1493:
1484:
1479:
1472:
1464:
1460:
1455:
1450:
1446:
1442:
1435:
1427:
1423:
1419:
1415:
1410:
1405:
1401:
1397:
1390:
1382:
1378:
1374:
1370:
1366:
1362:
1357:
1352:
1348:
1344:
1337:
1329:
1325:
1321:
1317:
1313:
1309:
1304:
1299:
1295:
1291:
1284:
1276:
1272:
1268:
1264:
1260:
1256:
1251:
1246:
1242:
1238:
1231:
1223:
1219:
1214:
1209:
1205:
1201:
1197:
1190:
1182:
1178:
1174:
1170:
1166:
1162:
1157:
1152:
1149:(5): 052301.
1148:
1144:
1137:
1129:
1125:
1121:
1117:
1113:
1109:
1105:
1101:
1097:
1090:
1082:
1078:
1074:
1070:
1066:
1062:
1058:
1054:
1050:
1043:
1035:
1031:
1027:
1023:
1019:
1015:
1011:
1007:
1003:
996:
988:
984:
977:
969:
965:
958:
950:
946:
942:
938:
934:
930:
926:
922:
918:
911:
903:
899:
892:
884:
880:
876:
872:
868:
864:
860:
853:
838:
832:
824:
820:
816:
812:
808:
804:
800:
793:
785:
781:
777:
773:
769:
762:
754:
747:
739:
735:
731:
727:
723:
719:
715:
711:
707:
700:
685:
681:
675:
667:
661:
653:
649:
643:
635:
629:
613:
609:
603:
599:
591:
586:Personal life
583:
581:
577:
573:
569:
565:
561:
557:
553:
548:
546:
542:
537:
533:
523:
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3170:James Arthur
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2718:Thomas Fiske
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2541:Arthur Jaffe
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136:Joel Feldman
132:Ezra Getzler
106:Institutions
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3270:1937 births
3244:(2023–2024)
3236:(2021–2022)
3228:(2019–2020)
3226:Jill Pipher
3220:(2017–2018)
3212:(2015–2016)
3204:(2013–2014)
3202:David Vogan
3196:(2011–2012)
3188:(2009–2010)
3180:(2007–2008)
3178:James Glimm
3172:(2005–2006)
3164:(2003–2004)
3156:(2001–2002)
3137:(1999–2000)
3129:(1997–1998)
3121:(1995–1996)
3113:(1993–1994)
3105:(1991–1992)
3097:(1989–1990)
3089:(1987–1988)
3081:(1985–1986)
3073:(1983–1984)
3065:(1981–1982)
3057:(1979–1980)
3049:(1977–1978)
3041:(1975–1976)
3039:Lipman Bers
3022:(1973–1974)
3014:(1971–1972)
3006:(1969–1970)
2998:(1967–1968)
2990:(1965–1966)
2982:(1963–1964)
2974:(1961–1962)
2966:(1959–1960)
2958:(1957–1958)
2950:(1955–1956)
2942:(1953–1954)
2934:(1951–1952)
2915:(1949–1950)
2907:(1947–1948)
2905:Einar Hille
2899:(1945–1946)
2891:(1943–1944)
2883:(1941–1942)
2875:(1939–1940)
2867:(1937–1938)
2859:(1935–1936)
2851:(1933–1934)
2843:(1931–1932)
2835:(1929–1930)
2827:(1927–1928)
2819:(1925–1926)
2800:(1923–1924)
2792:(1921–1922)
2784:(1919–1920)
2776:(1917–1918)
2768:(1915–1916)
2760:(1913–1914)
2752:(1911–1912)
2744:(1909–1910)
2736:(1907–1908)
2728:(1905–1906)
2720:(1903–1904)
2712:(1901–1902)
2710:E. H. Moore
2693:(1899–1900)
2685:(1897–1898)
2677:(1895–1896)
2669:(1891–1894)
2661:(1888–1890)
1804:(1): 1–14.
1557:1201.6003v2
1409:1305.6270v3
1012:(1): 1–34.
516:Frank Quinn
457:JLO cocycle
392:James Glimm
376:James Glimm
270: [
146:John Imbrie
65:Nationality
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3259:Categories
3154:Hyman Bass
3047:R. H. Bing
2188:2403.03272
1512:1602.02662
1483:1607.07126
594:References
53:1937-12-22
3242:Bryna Kra
3218:Ken Ribet
3146:2001–2024
3055:Peter Lax
3031:1975–2000
2924:1951–1974
2809:1925–1950
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2651:1888–1900
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1328:1424-0637
1303:1305.1792
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1250:1310.5370
1222:0022-1236
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883:0001-5962
823:1432-0916
738:1827-6121
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2571:Archived
2553:Archived
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