DOCSLIB.ORG

Arthur Jaffe Was Born 22 December 1937. He Received an AB In

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Arthur Jaffe Was Born 22 December 1937. He Received an AB In ARTHUR MICHAEL JAFFE Arthur Jaffe was born 22 December 1937. He received an AB in Chemistry from Princeton University in 1959, a BA in Mathematics from Cambridge University in 1961 where he was a Marshall Scholar, and a PhD in Physics from Princeton University under the direction of Arthur Wightman in 1966, where he was an NSF Fellow. Principal Positions since 1965: NAS-NRC Postdoctoral Fellow 1965—1967 Acting Assistant Professor of Mathematics, Stanford University 1966—1967 Assistant Professor of Physics, Harvard University 1967—1969 Associate Professor of Physics, Harvard University 1969—1970 Professor of Physics, Harvard University 1970—1975 Professor of Mathematical Physics, Harvard University 1975—1985 Landon T. Clay Professor of Mathematics and Theoretical Science, Harvard University 1985— Visiting Professorships: E.T.H. Zurich, Princeton University, Rockefeller University, University of California San Diego, Collège de France, Boston University, University of Rome Recognition: Mathematics and Physics PriZe, New York Academy of Science Dannie Heinemann PriZe, American Institute of Physics Fellow: AAAS, APS, AMS, SIAM Fellow, American Academy of Arts and Sciences Medal, Collège de France Member, U.S. National Academy of Sciences Honorary Member, Royal Irish Academy Principal Service: Cofounder and OrganiZer, Cargèse Schools of Mathematical Physics 1974—1996 Chief Editor, Communications in Mathematical Physics 1979—2000 Member of the “David Committee” of the NRC 1980—1983 Chair, Harvard Department of Mathematics 1987—1990 President, International Association of Mathematical Physics 1991—1996 President, American Mathematical Society 1997—1998 Cofounder and President, Clay Mathematics Institute 1998—2002 Chair, Council of Scientific Society Presidents 2000 Acting Chair, President’s Commission for the National Medal of Science 2001—2002 Chair of the Board, Dublin Institute for Advanced Study School of Theoretical Physics 2005—2020 Member Advisory Board, John Templeton Foundation 2010—2012, 2014—2016 Member Editorial Board, China Science Mathematics 2018— Distinguished Visiting Professor, Academy of Mathematics and Systems Science, CAS 2018— Scientific Advisory Board, Zapata Computing 2020— .
Load more

Recommended publications
  • Defining Physics at Imaginary Time: Reflection Positivity for Certain
    Defining physics at imaginary time: reflection positivity for certain Riemannian manifolds A thesis presented by Christian Coolidge Anderson [email protected] (978) 204-7656 to the Department of Mathematics in partial fulfillment of the requirements for an honors degree. Advised by Professor Arthur Jaffe. Harvard University Cambridge, Massachusetts March 2013 Contents 1 Introduction 1 2 Axiomatic quantum field theory 2 3 Definition of reflection positivity 4 4 Reflection positivity on a Riemannian manifold M 7 4.1 Function space E over M ..................... 7 4.2 Reflection on M .......................... 10 4.3 Reflection positive inner product on E+ ⊂ E . 11 5 The Osterwalder-Schrader construction 12 5.1 Quantization of operators . 13 5.2 Examples of quantizable operators . 14 5.3 Quantization domains . 16 5.4 The Hamiltonian . 17 6 Reflection positivity on the level of group representations 17 6.1 Weakened quantization condition . 18 6.2 Symmetric local semigroups . 19 6.3 A unitary representation for Glor . 20 7 Construction of reflection positive measures 22 7.1 Nuclear spaces . 23 7.2 Construction of nuclear space over M . 24 7.3 Gaussian measures . 27 7.4 Construction of Gaussian measure . 28 7.5 OS axioms for the Gaussian measure . 30 8 Reflection positivity for the Laplacian covariance 31 9 Reflection positivity for the Dirac covariance 34 9.1 Introduction to the Dirac operator . 35 9.2 Proof of reflection positivity . 38 10 Conclusion 40 11 Appendix A: Cited theorems 40 12 Acknowledgments 41 1 Introduction Two concepts dominate contemporary physics: relativity and quantum me- chanics. They unite to describe the physics of interacting particles, which live in relativistic spacetime while exhibiting quantum behavior.
    [Show full text]
  • Mathematisches Forschungsinstitut Oberwolfach Reflection Positivity
    Mathematisches Forschungsinstitut Oberwolfach Report No. 55/2017 DOI: 10.4171/OWR/2017/55 Reflection Positivity Organised by Arthur Jaffe, Harvard Karl-Hermann Neeb, Erlangen Gestur Olafsson, Baton Rouge Benjamin Schlein, Z¨urich 26 November – 2 December 2017 Abstract. The main theme of the workshop was reflection positivity and its occurences in various areas of mathematics and physics, such as Representa- tion Theory, Quantum Field Theory, Noncommutative Geometry, Dynamical Systems, Analysis and Statistical Mechanics. Accordingly, the program was intrinsically interdisciplinary and included talks covering different aspects of reflection positivity. Mathematics Subject Classification (2010): 17B10, 22E65, 22E70, 81T08. Introduction by the Organisers The workshop on Reflection Positivity was organized by Arthur Jaffe (Cambridge, MA), Karl-Hermann Neeb (Erlangen), Gestur Olafsson´ (Baton Rouge) and Ben- jamin Schlein (Z¨urich) during the week November 27 to December 1, 2017. The meeting was attended by 53 participants from all over the world. It was organized around 24 lectures each of 50 minutes duration representing major recent advances or introducing to a specific aspect or application of reflection positivity. The meeting was exciting and highly successful. The quality of the lectures was outstanding. The exceptional atmosphere of the Oberwolfach Institute provided the optimal environment for bringing people from different areas together and to create an atmosphere of scientific interaction and cross-fertilization. In particular, people from different subcommunities exchanged ideas and this lead to new col- laborations that will probably stimulate progress in unexpected directions. 3264 Oberwolfach Report 55/2017 Reflection positivity (RP) emerged in the early 1970s in the work of Osterwalder and Schrader as one of their axioms for constructive quantum field theory ensuring the equivalence of their euclidean setup with Wightman fields.
    [Show full text]
  • Partial Differential Equations
    CALENDAR OF AMS MEETINGS THIS CALENDAR lists all meetings which have been approved by the Council pnor to the date this issue of the Nouces was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet­ ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab­ stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions. MEETING ABSTRACT NUMBER DATE PLACE DEADLINE ISSUE 778 June 20-21, 1980 Ellensburg, Washington APRIL 21 June 1980 779 August 18-22, 1980 Ann Arbor, Michigan JUNE 3 August 1980 (84th Summer Meeting) October 17-18, 1980 Storrs, Connecticut October 31-November 1, 1980 Kenosha, Wisconsin January 7-11, 1981 San Francisco, California (87th Annual Meeting) January 13-17, 1982 Cincinnati, Ohio (88th Annual Meeting) Notices DEADLINES ISSUE NEWS ADVERTISING June 1980 April 18 April 29 August 1980 June 3 June 18 Deadlines for announcements intended for the Special Meetings section are the same as for News.
    [Show full text]
  • 6. L CPT Reversal
    6. CPT reversal l Précis. On the representation view, there may be weak and strong arrows of time. A weak arrow exists. A strong arrow might too, but not in current physics due to CPT symmetry. There are many ways to reverse time besides the time reversal operator T. Writing P for spatial reflection or ‘parity’, and C for matter-antimatter exchange or ‘charge conjugation’, we find that PT, CT, and CPT are all time reversing transformations, when they exist. More generally, for any non-time-reversing (unitary) transformation U, we find that UT is time reversing. Are any of these transformations relevant for the arrow of time? Feynman (1949) captured many of our imaginations with the proposal that to understand the direction of time, we must actually consider the exchange of matter and antimatter as well.1 Writing about it years later, he said: “A backwards-moving electron when viewed with time moving forwards appears the same as an ordinary electron, except it’s attracted to normal electrons — we say it has positive charge. For this reason it’s called a ‘positron’. The positron is a sister to the electron, and it is an example of an ‘anti-particle’. This phenomenon is quite general. Every particle in Nature has an amplitude to move backwards in time, and therefore has an anti-particle.”(Feynman 1985, p.98) Philosophers Arntzenius and Greaves (2009, p.584) have defended Feynman’s proposal, 1In his Nobel prize speech, Feynman (1972, pg.163) attributes this idea to Wheeler in the development of their absorber theory (Wheeler and Feynman 1945).
    [Show full text]
  • Arthur Strong Wightman (1922–2013)
    Obituary Arthur Strong Wightman (1922–2013) Arthur Wightman, a founding father of modern mathematical physics, passed away on January 13, 2013 at the age of 90. His own scientific work had an enormous impact in clar- ifying the compatibility of relativity with quantum theory in the framework of quantum field theory. But his stature and influence was linked with an enormous cadre of students, scientific collaborators, and friends whose careers shaped fields both in mathematics and theoretical physics. Princeton has a long tradition in mathematical physics, with university faculty from Sir James Jeans through H.P. Robertson, Hermann Weyl, John von Neumann, Eugene Wigner, and Valentine Bargmann, as well as a long history of close collaborations with colleagues at the Institute for Advanced Study. Princeton became a mecca for quantum field theorists as well as other mathematical physicists during the Wightman era. Ever since the advent of “axiomatic quantum field theory”, many researchers flocked to cross the threshold of his open office door—both in Palmer and later in Jadwin—for Arthur was renowned for his generosity in sharing ideas and research directions. In fact, some students wondered whether Arthur might be too generous with his time helping others, to the extent that it took time away from his own research. Arthur had voracious intellectual appetites and breadth of interests. Through his interactions with others and his guidance of students and postdocs, he had profound impact not only on axiomatic and constructive quantum field theory but on the de- velopment of the mathematical approaches to statistical mechanics, classical mechanics, dynamical systems, transport theory, non-relativistic quantum mechanics, scattering the- ory, perturbation of eigenvalues, perturbative renormalization theory, algebraic quantum field theory, representations of C⇤-algebras, classification of von Neumann algebras, and higher spin equations.
    [Show full text]
  • 1995 Steele Prizes
    steele.qxp 4/27/98 3:29 PM Page 1288 1995 Steele Prizes Three Leroy P. Steele Prizes were presented at The text that follows contains, for each award, the awards banquet during the Summer Math- the committee’s citation, the recipient’s response fest in Burlington, Vermont, in early August. upon receiving the award, and a brief bio- These prizes were established in 1970 in honor graphical sketch of the recipient. of George David Birkhoff, William Fogg Osgood, and William Caspar Graustein Edward Nelson: 1995 Steele Prize for and are endowed under the Seminal Contribution to Research terms of a bequest from The 1995 Leroy P. Steele award for research of Leroy P. Steele. seminal importance goes to Professor Edward The Steele Prizes are Nelson of Princeton University for the following ...for a research awarded in three categories: two papers in mathematical physics character- for a research paper of fun- ized by leaders of the field as extremely innov- paper of damental and lasting impor- ative: tance, for expository writing, 1. “A quartic interaction in two dimensions” in fundamental and for cumulative influence Mathematical Theory of Elementary Particles, and lasting extending over a career, in- MIT Press, 1966, pages 69–73; cluding the education of doc- 2. “Construction of quantum fields from Markoff importance, toral students. The current fields” in Journal of Functional Analysis 12 award is $4,000 in each cate- (1973), 97–112. for expository gory. In these papers he showed for the first time The recipients of the 1995 how to use the powerful tools of probability writing, and for Steele Prizes are Edward Nel- theory to attack the hard analytic questions of son for seminal contribution constructive quantum field theory, controlling cumulative to research, Jean-Pierre Serre renormalizations with Lp estimates in the first influence for mathematical exposition, paper and, in the second, turning Euclidean and John T.
    [Show full text]
  • Solutions in Constructive Field Theory
    Solutions in Constructive Field Theory Leif Hancox-Li ∗ [email protected] June 7, 2016 Abstract Constructive field theory aims to rigorously construct concrete, non-trivial solutions to Lagrangians used in particle physics, where the solutions satisfy some relevant set of axioms. I examine the relationship of solutions in constructive field theory to both axiomatic and Lagrangian quantum field theory (QFT). I argue that Lagrangian QFT provides conditions for what counts as a successful constructive solution, and that it provides other information that guides constructive field theorists to solutions. Solutions matter because they describe the behavior of QFT systems, and thus what QFT says the world is like. Constructive field theory, in incorporating ingredients from both axiomatic and Lagrangian QFT, clarifies existing disputes about which parts of QFT are philosophically relevant and how rigor relates to these disputes. ∗I thank Bob Batterman and Michael Miller for comments and encouragement. Several anonymous referees also contribued valuable comments. Copyright Philosophy of Science 2016 Preprint (not copyedited or formatted) Please use DOI when citing or quoting 1 Introduction To date, philosophers of quantum field theory (QFT) have paid much attention to roughly two kinds of QFT: axiomatic approaches to algebraic QFT (Halvorson and Muger,¨ 2006), and Lagrangian-based QFT as used by particle physicists (Wallace, 2006). Comparatively less attention, however, has been paid to constructive QFT, an approach that aims to rigorously construct non-trivial solutions of QFT for Lagrangians and Hamiltonians that are important in particle physics, ensuring that such solutions satisfy certain axioms. In doing so, constructive QFT mediates between axiomatic approaches to QFT and physicists’ Lagrangian-based QFT.
    [Show full text]
  • Reflections and Twists *
    PUBLICATIONS MATHÉMATIQUES DE L’I.H.É.S. ARTHUR JAFFE Reflections and twists Publications mathématiques de l’I.H.É.S., tome S88 (1998), p. 119-130 <http://www.numdam.org/item?id=PMIHES_1998__S88__119_0> © Publications mathématiques de l’I.H.É.S., 1998, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions géné- rales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou im- pression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ REFLECTIONS AND TWISTS * by ARTHUR JAFFE I. Lif e as a student My extraordinary first-hand introduction to the Feldverein took place 35 years ago, during the year 1 spent at the IHÉS. The path 1 followed from Princeton to Bures-sur-Yvette had a definite random element, so please bear with a bit of autobiographical perspective. 1 began as an undergraduate majoring in experimental chemistry, originally thinking of going into medicine, but eventually moving toward the goal to become a theoretical chemist. With luck, 1 received a Marshall Scholarship to do just that in Cambridge, and upon advice from my undergraduate mentor Charles Gillispie, 1 applied and was admitted to Clare College. But the spring before sailing with the other Marshall scholars to Southampton on the QE II, second thoughts surfaced about continuing in chemistry.
    [Show full text]
  • Solutions in Constructive Field Theory
    Solutions in Constructive Field Theory Bihui Li [email protected] April 26, 2016 Abstract Constructive field theory aims to rigorously construct concrete solutions to Lagrangians used in particle physics, where the solutions satisfy some relevant set of axioms. I examine the nature of solutions in constructive field theory and their relationship to both axiomatic and Lagrangian quantum field theory (QFT). I argue that Lagrangian QFT provides conditions for what counts as a successful constructive solution, and that it provides other important information that guides constructive field theorists to solutions. Solutions matter because they describe the behavior of systems in QFT, and thus what QFT says the world is like. Constructive field theory, in incorporating ingredients from both axiomatic and Lagrangian QFT, clarifies existing disputes about which parts of QFT are relevant to philosophers and the role of rigor in these disputes. 1 1 Introduction To date, philosophers of quantum field theory (QFT) have paid much attention to roughly two kinds of QFT: axiomatic approaches to algebraic QFT (Halvorson & M¨uger,2006), and Lagrangian-based QFT as used by particle physicists (Wallace, 2006). Comparatively less attention, however, has been paid to constructive QFT, an approach that aims to rigorously construct solutions of QFT for Lagrangians and Hamiltons that are important in particle physics, ensuring that such solutions satisfy certain axioms. In doing so, constructive QFT mediates between axiomatic approaches to QFT (of which algebraic QFT is one kind) and physicists' Lagrangian-based QFT. It ensures that the various axiom systems have a physically meaningful correspondence with the world. Since we usually take solutions in physical theories to describe the behavior of systems falling under the theory and constructive QFT aims to produce these solutions, constructive QFT deserves some philosophical attention.
    [Show full text]
  • History of RSB Interview: Francesco Guerra January 26, 2021, 8:30Am-10:30Pm (EST)
    History of RSB Interview: Francesco Guerra January 26, 2021, 8:30am-10:30pm (EST). Final revision: May 10, 2021 Interviewers: Patrick Charbonneau, Duke University, [email protected] Francesco Zamponi, ENS-Paris Location: Over Zoom, from Prof. Guerra’s second home in Genova, Italy. How to cite: P. Charbonneau, History of RSB Interview: Francesco Guerra, transcript of an oral history conducted 2021 by Patrick Charbonneau and Francesco Zamponi, History of RSB Project, CAPHÉS, École normale supérieure, Paris, 2021, 27 p. https://doi.org/10.34847/nkl.05bd6npc PC: Hello, Professor Guerra. Thank you very much for joining us. As we've dis- cussed, today we will be mostly discussing the history of replica symmetry breaking in a broad sense. Before we get there, however, we wanted to ask you a few questions about your background and interests. In particular, could you tell us what led you to be interested in physics and to pursue a Laurea degree in theoretical physics? FG: Like many people in Italy, in the first two years of university I was enrolled in engineering, like Ettore Majorana1 for example. Then I found that I was more interested in basic scientific questions, so I decided to shift to phys- ics. It was the start in Naples at the time—it was ‘62—of new, big enter- prises in physics. In Naples, there was the old institute of physics and they were involved mostly in classical physics, spectroscopy, solid state physics, and so on. Then, in the middle of the ‘50s, modern physics underwent an impressive development. My big boss at the time was Eduardo Caianiello2.
    [Show full text]
  • Tao's Method, the Casimir Effect and Interacting Wightman Theories
    Perturbative versus non-perturbative quantum field theory: Tao’s method, the Casimir effect and interacting Wightman theories Walter Felipe Wreszinski, Instituto de F´ısica, Universidade de S˜ao Paulo, 05508-090 S˜ao Paulo, SP, Brasil, [email protected] July 6, 2021 Abstract We dwell upon certain points concerning the meaning of quantum field theory: the problems with the perturbative approach, and the question raised by ’t Hooft of the existence of the theory in a well- defined (rigorous) mathematical sense, as well as some of the few ex- istent mathematically precise results on fully quantized field theories. Emphasis is brought on how the mathematical contributions help to elucidate or illuminate certain conceptual aspects of the theory when applied to real physical phenomena, in particular, the singular nature of quantum fields. In a first part, we present a comprehensive review of divergent versus asymptotic series, with qed as background example, as well as a method due to Terence Tao which conveys mathematical sense to divergent series. In a second part we apply Tao’s method to arXiv:2101.03930v4 [math-ph] 4 Jul 2021 the Casimir effect in its simplest form, consisting of perfectly conduct- ing parallel plates, arguing that the usual theory, which makes use of the Euler-MacLaurin formula, still contains a residual infinity, which is eliminated in our approach. In the third part, we revisit the general theory of nonperturbative quantum fields, in the form of newly pro- posed (with Christian Jaekel) Wightman axioms for interacting field theories, with applications to “dressed” electrons in a theory with massless particles (such as qed), as well as unstable particles.
    [Show full text]
  • Nine Lessons of My Teacher, Arthur Strong Wightman a Talk at Princeton University, 10 March 2013 by Arthur Jaffe (Cambridge (MA), Basel, and Z¨Urich)
    Nine Lessons of my Teacher, Arthur Strong Wightman Nine Lessons of my Teacher, Arthur Strong Wightman A Talk at Princeton University, 10 March 2013 by Arthur Jaffe (Cambridge (MA), Basel, and Z¨urich) At Harvard University, Arthur Ja↵e is the Landon T. Clay Pro- fessor of Mathematics and Theoretical Science. He is currently on sabbatical leave at the University of Basel and at the ETH, Z¨urich. He has worked in several fields of mathematical physics. Arthur Ja↵e received his doctorate in physics from Princeton as a student of Arthur Wightman, after studying mathematics as a Cambridge undergraduate and chemistry as a Princeton un- dergraduate. He has served as president of IAMP, and also as president of the American Mathematical Society. Preamble. All of us here today have been students of Arthur Wightman. But his thirty-six formal doctoral students form a very special club, which I represent on this part of today’s program. A few members appear in this 1965 snapshot of Arthur Wightman’s seminar in Palmer 301, with Arthur smiling benevolently in the center. IAMP News Bulletin, April 2013 3 Arthur Ja↵e Postdoctoral fellows and other visitors to Princeton surround the students during those exciting times some 48 years ago. To the best of my knowledge, here is the complete, wide-ranging list of graduate students: Arthur Wightman’s student club Silvan Samuel Schweber 1952 Gerald Goldin 1969 Richard Ferrell 1952 Eugene Speer 1969 Douglas Hall 1957 George Svetlichny 1969 Oscar W. Greenberg 1957 Barry Simon 1970 Huzihiro Araki 1960 Charles Newman 1971 John S.
    [Show full text]