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Arthur Jaffe began as chief editor of ''[[Communications in Mathematical Physics]]'' in 1979 and served for 21 years until 2001. He is a distinguished visiting professor at the [http://english.amss.cas.cn Academy of Mathematics and Systems Science] of the [[Chinese Academy of Sciences]].
Arthur Jaffe began as chief editor of ''[[Communications in Mathematical Physics]]'' in 1979 and served for 21 years until 2001. He is a distinguished visiting professor at the [http://english.amss.cas.cn Academy of Mathematics and Systems Science] of the [[Chinese Academy of Sciences]].


==Contributions==
==Research==

With [[James Glimm]], he founded the subject called [[constructive quantum field theory]]. They established existence theorems for two- and three-dimensional examples of non-linear, relativistic quantum fields.
=== Nonpositivity of Energy Density ===
One of Arthur Jaffe's earliest contributions was his proof, along with Henry Epstein and [[Vladimir Jurko Glaser|Vladimir Glaser]], that energy densities in [[Quantum field theory|local quantum field theories]] are always nonpositive<ref>{{Cite journal |last=Epstein |first=H. |last2=Glaser |first2=V. |last3=Jaffe |first3=A. |date=1965-04-01 |title=Nonpositivity of the energy density in quantized field theories |url=https://doi.org/10.1007/BF02749799 |journal=Il Nuovo Cimento (1955-1965) |language=en |volume=36 |issue=3 |pages=1016–1022 |doi=10.1007/BF02749799 |issn=1827-6121}}</ref>.

=== Constructive Quantum Field Theory ===
A large amount of Jaffe's work deals with the rigorous mathematical construction and [[Mathematical proof|proof]] 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 rigorously constructed was the [[Free field|free field model]]. In a series of landmark papers Jaffe and collaborators made great progress in understanding the nature of quantum field theory<ref>{{Cite journal |last=Jaffe |first=Arthur |date=1966 |title=Existence Theorems for a Cut-off λφ4 Field Theory |journal=Mathematical Theory of Elementary Particles |via=MIT Press}}</ref><ref>{{Cite journal |last=Glimm |first=James |last2=Jaffe |first2=Arthur |date=1968-12-25 |title=<nowiki>A $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ Quantum Field Theory without Cutoffs. I</nowiki> |url=https://link.aps.org/doi/10.1103/PhysRev.176.1945 |journal=Physical Review |volume=176 |issue=5 |pages=1945–1951 |doi=10.1103/PhysRev.176.1945}}</ref><ref>{{Cite journal |last=Cannon |first=John T. |last2=Jaffe |first2=Arthur M. |date=1970-12-01 |title=Lorentz covariance of the λ(ϕ4)2 quantum field theory |url=https://doi.org/10.1007/BF01646027 |journal=Communications in Mathematical Physics |language=en |volume=17 |issue=4 |pages=261–321 |doi=10.1007/BF01646027 |issn=1432-0916}}</ref><ref>{{Cite web |title=The $\lambda(\varphi^4)_2$ quantum field theory without cutoffs. II. The field operators and the approximate vacuum {{!}} Annals of Mathematics |url=https://annals.math.princeton.edu/1970/91-2/p04 |access-date=2024-04-19 |language=en-US}}</ref><ref>{{Cite journal |last=Glimm |first=James |last2=Jaffe |first2=Arthur |date=1970 |title=The λ(φ4)2 quantum field theory without cutoffsquantum field theory without cutoffs: III. The physical vacuum |url=https://projecteuclid.org/journals/acta-mathematica/volume-125/issue-none/The-%ce%bb%cf%8642-quantum-field-theory-without-cutoffsquantum-field-theory-without/10.1007/BF02392335.full |journal=Acta Mathematica |volume=125 |issue=none |pages=203–267 |doi=10.1007/BF02392335 |issn=0001-5962}}</ref><ref>{{Cite journal |last=Jaffe |first=Arthur |last2=Glimm |first2=James |date=1973 |title=Positivity of the φ43 Hamiltonian |journal=Fortschritte der Physik |volume=21}}</ref>, culminating in the first ever rigorous mathematical interacting local quantum field theory<ref>{{Cite journal |last=Glimm |first=James |last2=Jaffe |first2=Arthur |last3=Spencer |first3=Thomas |date=1974 |title=The Wightman Axioms and Particle Structure in the P(φ)2 Quantum Field Model |url=https://www.jstor.org/stable/1970959 |journal=Annals of Mathematics |volume=100 |issue=3 |pages=585–632 |doi=10.2307/1970959 |issn=0003-486X}}</ref>. For this work, Jaffe and [[James Glimm]] are acknowledged as the founders of the subject of [[constructive quantum field theory]].

=== Phase Transitions in Quantum Field Theory ===
Another notable contribution of Jaffe's is his proof, along with [[James Glimm]] and [[Thomas Spencer (mathematical physicist)|Thomas Spencer]], that quantum field theories can have [[Phase transition|phase transitions]]<ref>{{Cite journal |last=Jaffe |first=Arthur |last2=Glimm |first2=James |last3=Thomas |first3=Spencer |date=1975 |title=Phase Transitions for φ42 Quantum Fields |url=https://www.researchgate.net/publication/226829034_Phase_transitions_for_ph24_quantum_fields |journal=Communications in Mathematical Physics |issue=45 |pages=203-216}}</ref><ref>{{Cite journal |last=Jaffe |first=Arthur |last2=Glimm |first2=James |last3=Spencer |first3=Thomas |date=1976 |title=Existence of Phase Transitions for φ42 Quantum Fields |url=https://inspirehep.net/literature/2772 |journal=Mathematical Methods of Quantum Field Theory |via=CNRS}}</ref>.

=== Higgs Effect ===
Jaffe is also known for his mathematical proof of an aspect of the [[Higgs mechanism|abelian Higgs mechanism]]. Namely, he showed that [[symmetry breaking]] in the abelian Higgs model induces a gap in the [[mass spectrum]]<ref>{{Citation |last=Balaban |first=Tadeusz |title=Renormalization of the Higgs Model: Minimizers, Propagators and the Stability of Mean Field Theory |date=1985 |work=Quantum Field Theory: A Selection of Papers in Memoriam Kurt Symanzik |pages=299–329 |editor-last=Jaffe |editor-first=Arthur |url=https://doi.org/10.1007/978-3-642-70307-2_17 |access-date=2024-04-20 |place=Berlin, Heidelberg |publisher=Springer |language=en |doi=10.1007/978-3-642-70307-2_17 |isbn=978-3-642-70307-2 |last2=Imbrie |first2=John |last3=Jaffe |first3=Arthur |editor2-last=Lehmann |editor2-first=Harry |editor3-last=Mack |editor3-first=Gerhard}}</ref><ref>{{Cite journal |last=Jaffe |first=Arthur |last2=Imbrie |first2=John |last3=Balaban |first3=Tadeusz |date=1988 |title=Effective Action and Cluster Properties of the Abelian Higgs Model |url=https://uva.theopenscholar.com/files/john-imbrie/files/effectiveaction.pdf |journal=Communications in Mathematical Physics |pages=257-315}}</ref><ref>{{Cite journal |last=Balaban |first=Tadeusz |last2=Imbrie |first2=John |last3=Jaffe |first3=Arthur |last4=Brydges |first4=David |date=1984-12-01 |title=The mass gap for Higgs models on a unit lattice |url=https://ui.adsabs.harvard.edu/abs/1984AnPhy.158..281B |journal=Annals of Physics |volume=158 |pages=281–319 |doi=10.1016/0003-4916(84)90121-0 |issn=0003-4916}}</ref>.

=== Supersymmetric Models ===
Within his work on [[Supersymmetry|supersymmetric quantum field theories]] Jaffe is most known for introducing the [[JLO cocycle]], along with collaborators Andrzej Lesniewski and [[Konrad Osterwalder]]<ref>{{Cite journal |last=Kastler |first=D. |date=1990 |editor-last=Doebner |editor-first=H. -D. |editor2-last=Hennig |editor2-first=J. -D. |title=KMS states, cyclic cohomology and supersymmetry |url=https://link.springer.com/chapter/10.1007/3-540-53503-9_55 |journal=Quantum Groups |language=en |location=Berlin, Heidelberg |publisher=Springer |pages=375–397 |doi=10.1007/3-540-53503-9_55 |isbn=978-3-540-46647-5}}</ref><ref>{{Cite journal |last=Jaffe |first=Arthur |last2=Lesniewski |first2=Andrzej |last3=Osterwalder |first3=Konrad |date=1988 |title=Quantum $K$-theory. I. The Chern character |url=https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-118/issue-1/Quantum-K-theory-I-The-Chern-character/cmp/1104161905.full |journal=Communications in Mathematical Physics |volume=118 |issue=1 |pages=1–14 |issn=0010-3616}}</ref>. The JLO construction takes as input a supersymmetric quantum field theory (mathematically, a θ-summable [[spectral triple]]) and outputs a cocylce in [[Alain Connes|Alain Connes']] [[Cyclic homology|cyclic cohomology]].

=== Quantum Information ===
In his later years, Arthur Jaffe has made varied contributions to the theory of [[quantum information]]<ref>{{Cite web |last=Jaffe |first=Arthur |last2=Liu |first2=Zhengwei |last3=Wozniakowski |first3=Alex |date=2016-05-01 |title=Compressed Teleportation |url=https://arxiv.org/abs/1605.00321v1 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref><ref>{{Cite web |last=Jaffe |first=Arthur |last2=Liu |first2=Zhengwei |last3=Wozniakowski |first3=Alex |date=2016-11-19 |title=Constructive Simulation and Topological Design of Protocols |url=https://arxiv.org/abs/1611.06447v2 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref><ref>{{Cite web |last=Jaffe |first=Arthur |last2=Liu |first2=Zhengwei |last3=Wozniakowski |first3=Alex |date=2016-04-30 |title=Holographic Software for Quantum Networks |url=https://arxiv.org/abs/1605.00127v5 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref><ref>{{Cite web |last=Li |first=Lu |last2=Bu |first2=Kaifeng |last3=Koh |first3=Dax Enshan |last4=Jaffe |first4=Arthur |last5=Lloyd |first5=Seth |date=2022-08-12 |title=Wasserstein Complexity of Quantum Circuits |url=https://arxiv.org/abs/2208.06306v1 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref>. Notably among these contributions are the introduction of quantum [[Fourier analysis]]<ref>{{Cite web |last=Jaffe |first=Arthur |last2=Jiang |first2=Chunlan |last3=Liu |first3=Zhengwei |last4=Ren |first4=Yunxiang |last5=Wu |first5=Jinsong |date=2020-02-10 |title=Quantum Fourier Analysis |url=https://arxiv.org/abs/2002.03477v1 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref><ref>{{Cite web |last=Bu |first=Kaifeng |last2=Gu |first2=Weichen |last3=Jaffe |first3=Arthur |date=2023-02-16 |title=Discrete Quantum Gaussians and Central Limit Theorem |url=https://arxiv.org/abs/2302.08423v2 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref>, the study of quantum resources<ref>{{Cite web |last=Bu |first=Kaifeng |last2=Gu |first2=Weichen |last3=Jaffe |first3=Arthur |date=2023-06-15 |title=Stabilizer Testing and Magic Entropy |url=https://arxiv.org/abs/2306.09292v1 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref><ref>{{Cite web |last=Chen |first=Liyuan |last2=Garcia |first2=Roy J. |last3=Bu |first3=Kaifeng |last4=Jaffe |first4=Arthur |date=2022-11-18 |title=Magic of Random Matrix Product States |url=https://arxiv.org/abs/2211.10350v3 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref><ref>{{Cite web |last=Garcia |first=Roy J. |last2=Bu |first2=Kaifeng |last3=Jaffe |first3=Arthur |date=2022-08-22 |title=Resource theory of quantum scrambling |url=https://arxiv.org/abs/2208.10477v2 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref>, and the introduction of the 3D [[String diagram|graphical language]] for quantum information<ref>{{Cite web |last=Liu |first=Zhengwei |last2=Wozniakowski |first2=Alex |last3=Jaffe |first3=Arthur |date=2016-12-08 |title=Quons: A 3D Language for Quantum Information |url=https://arxiv.org/abs/1612.02630v3 |access-date=2024-04-20 |website=arXiv.org |language=en}}</ref>.


==Awards and honors==
==Awards and honors==
Awarded the [[Dannie Heineman Prize for Mathematical Physics]] in 1980. In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-26.</ref>
In 190 Arthur Jaffe was awarded the [[Dannie Heineman Prize for Mathematical Physics]]. In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2013-01-26.</ref>


==Personal life==
==Personal life==

Revision as of 00:58, 20 April 2024

Arthur M. Jaffe
Arthur Jaffe at his office in 2005
Born (1937-12-22) December 22, 1937 (age 86)
NationalityAmerican
Alma materPrinceton University
Clare College, Cambridge
Scientific career
FieldsMathematical physics
InstitutionsHarvard University
Doctoral advisorArthur Wightman
Doctoral studentsEzra Getzler
Joel Feldman
Clifford Taubes

Arthur Michael Jaffe (/ˈdʒæfi/; born December 22, 1937) is an American mathematical physicist at Harvard University, where in 1985 he succeeded George Mackey as the Landon T. Clay Professor of Mathematics and Theoretical Science.[1]

Education and career

After graduating from Pelham Memorial High School in 1955,[2] Jaffe attended Princeton University as an undergraduate obtaining a degree in chemistry in 1959, and later Clare College, Cambridge, as a Marshall Scholar, obtaining a degree in mathematics in 1961. He then returned to Princeton, obtaining a doctorate in physics in 1966 with Arthur Wightman. His whole career has been spent teaching mathematical physics and pursuing research at Harvard University. His 26 doctoral students include Joel Feldman, Ezra Getzler, and Clifford Taubes. He has had many post-doctoral collaborators, including Robert Schrader, Konrad Osterwalder, Juerg Froehlich, Roland Sénéor [fr], Thomas Spencer, and Antti Kupiainen.

For several years Jaffe was president of the International Association of Mathematical Physics, and later of the American Mathematical Society. He chaired the Council of Scientific Society Presidents. He presently serves as chair of the board of the Dublin Institute for Advanced Studies, School of Theoretical Physics.

Jaffe conceived the idea of the Clay 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.

Arthur Jaffe began as chief editor of Communications in Mathematical Physics in 1979 and served for 21 years until 2001. He is a distinguished visiting professor at the Academy of Mathematics and Systems Science of the Chinese Academy of Sciences.

Research

Nonpositivity of Energy Density

One of Arthur Jaffe's earliest contributions was his proof, along with Henry Epstein and Vladimir Glaser, that energy densities in local quantum field theories are always nonpositive[3].

Constructive Quantum Field Theory

A large amount of Jaffe's work deals with the rigorous mathematical construction and proof 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 rigorously constructed was the free field model. In a series of landmark papers Jaffe and collaborators made great progress in understanding the nature of quantum field theory[4][5][6][7][8][9], culminating in the first ever rigorous mathematical interacting local quantum field theory[10]. For this work, Jaffe and James Glimm are acknowledged as the founders of the subject of constructive quantum field theory.

Phase Transitions in Quantum Field Theory

Another notable contribution of Jaffe's is his proof, along with James Glimm and Thomas Spencer, that quantum field theories can have phase transitions[11][12].

Higgs Effect

Jaffe is also known for his mathematical proof of an aspect of the abelian Higgs mechanism. Namely, he showed that symmetry breaking in the abelian Higgs model induces a gap in the mass spectrum[13][14][15].

Supersymmetric Models

Within his work on supersymmetric quantum field theories Jaffe is most known for introducing the JLO cocycle, along with collaborators Andrzej Lesniewski and Konrad Osterwalder[16][17]. The JLO construction takes as input a supersymmetric quantum field theory (mathematically, a θ-summable spectral triple) and outputs a cocylce in Alain Connes' cyclic cohomology.

Quantum Information

In his later years, Arthur Jaffe has made varied contributions to the theory of quantum information[18][19][20][21]. Notably among these contributions are the introduction of quantum Fourier analysis[22][23], the study of quantum resources[24][25][26], and the introduction of the 3D graphical language for quantum information[27].

Awards and honors

In 190 Arthur Jaffe was awarded the Dannie Heineman Prize for Mathematical Physics. In 2012 he became a fellow of the American Mathematical Society.[28]

Personal life

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.

References

  1. ^ "Website of ACAP". Archived from the original on 13 July 2019. Retrieved 19 March 2018.
  2. ^ "Oral History Interviews. Arthur Jaffe, interviewed by Katherine Sopka". American Institute of Physics. 15 February 1977.
  3. ^ Epstein, H.; Glaser, V.; Jaffe, A. (1 April 1965). "Nonpositivity of the energy density in quantized field theories". Il Nuovo Cimento (1955-1965). 36 (3): 1016–1022. doi:10.1007/BF02749799. ISSN 1827-6121.
  4. ^ Jaffe, Arthur (1966). "Existence Theorems for a Cut-off λφ4 Field Theory". Mathematical Theory of Elementary Particles – via MIT Press.
  5. ^ Glimm, James; Jaffe, Arthur (25 December 1968). "A $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ Quantum Field Theory without Cutoffs. I". Physical Review. 176 (5): 1945–1951. doi:10.1103/PhysRev.176.1945.
  6. ^ 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. ISSN 1432-0916.
  7. ^ "The $\lambda(\varphi^4)_2$ quantum field theory without cutoffs. II. The field operators and the approximate vacuum | Annals of Mathematics". Retrieved 19 April 2024.
  8. ^ Glimm, James; Jaffe, Arthur (1970). "The λ(φ4)2 quantum field theory without cutoffsquantum field theory without cutoffs: III. The physical vacuum". Acta Mathematica. 125 (none): 203–267. doi:10.1007/BF02392335. ISSN 0001-5962.
  9. ^ Jaffe, Arthur; Glimm, James (1973). "Positivity of the φ43 Hamiltonian". Fortschritte der Physik. 21.
  10. ^ 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. ISSN 0003-486X.
  11. ^ Jaffe, Arthur; Glimm, James; Thomas, Spencer (1975). "Phase Transitions for φ42 Quantum Fields". Communications in Mathematical Physics (45): 203–216.
  12. ^ Jaffe, Arthur; Glimm, James; Spencer, Thomas (1976). "Existence of Phase Transitions for φ42 Quantum Fields". Mathematical Methods of Quantum Field Theory – via CNRS.
  13. ^ 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, ISBN 978-3-642-70307-2, retrieved 20 April 2024
  14. ^ Jaffe, Arthur; Imbrie, John; Balaban, Tadeusz (1988). "Effective Action and Cluster Properties of the Abelian Higgs Model" (PDF). Communications in Mathematical Physics: 257–315.
  15. ^ Balaban, Tadeusz; Imbrie, John; Jaffe, Arthur; Brydges, David (1 December 1984). "The mass gap for Higgs models on a unit lattice". Annals of Physics. 158: 281–319. doi:10.1016/0003-4916(84)90121-0. ISSN 0003-4916.
  16. ^ Kastler, D. (1990). Doebner, H. -D.; Hennig, J. -D. (eds.). "KMS states, cyclic cohomology and supersymmetry". Quantum Groups. Berlin, Heidelberg: Springer: 375–397. doi:10.1007/3-540-53503-9_55. ISBN 978-3-540-46647-5.
  17. ^ Jaffe, Arthur; Lesniewski, Andrzej; Osterwalder, Konrad (1988). "Quantum $K$-theory. I. The Chern character". Communications in Mathematical Physics. 118 (1): 1–14. ISSN 0010-3616.
  18. ^ Jaffe, Arthur; Liu, Zhengwei; Wozniakowski, Alex (1 May 2016). "Compressed Teleportation". arXiv.org. Retrieved 20 April 2024.
  19. ^ Jaffe, Arthur; Liu, Zhengwei; Wozniakowski, Alex (19 November 2016). "Constructive Simulation and Topological Design of Protocols". arXiv.org. Retrieved 20 April 2024.
  20. ^ Jaffe, Arthur; Liu, Zhengwei; Wozniakowski, Alex (30 April 2016). "Holographic Software for Quantum Networks". arXiv.org. Retrieved 20 April 2024.
  21. ^ Li, Lu; Bu, Kaifeng; Koh, Dax Enshan; Jaffe, Arthur; Lloyd, Seth (12 August 2022). "Wasserstein Complexity of Quantum Circuits". arXiv.org. Retrieved 20 April 2024.
  22. ^ Jaffe, Arthur; Jiang, Chunlan; Liu, Zhengwei; Ren, Yunxiang; Wu, Jinsong (10 February 2020). "Quantum Fourier Analysis". arXiv.org. Retrieved 20 April 2024.
  23. ^ Bu, Kaifeng; Gu, Weichen; Jaffe, Arthur (16 February 2023). "Discrete Quantum Gaussians and Central Limit Theorem". arXiv.org. Retrieved 20 April 2024.
  24. ^ Bu, Kaifeng; Gu, Weichen; Jaffe, Arthur (15 June 2023). "Stabilizer Testing and Magic Entropy". arXiv.org. Retrieved 20 April 2024.
  25. ^ Chen, Liyuan; Garcia, Roy J.; Bu, Kaifeng; Jaffe, Arthur (18 November 2022). "Magic of Random Matrix Product States". arXiv.org. Retrieved 20 April 2024.
  26. ^ Garcia, Roy J.; Bu, Kaifeng; Jaffe, Arthur (22 August 2022). "Resource theory of quantum scrambling". arXiv.org. Retrieved 20 April 2024.
  27. ^ Liu, Zhengwei; Wozniakowski, Alex; Jaffe, Arthur (8 December 2016). "Quons: A 3D Language for Quantum Information". arXiv.org. Retrieved 20 April 2024.
  28. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-26.

External links

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