DOCSLIB.ORG

Lecture Notes in Physics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Lecture Notes in Physics Lecture Notes in Physics Edited by J. Ehlers, MCinchen,K. Hepp, ZiJrich, and H. A. WeidenmCiller, Heidelberg Managing Editor: W. BeiglbSck, Heidelberg 39 International Symposium on Mathematical Problems in Theoretical Physics January 23-29, 1975, Kyoto University, Kyoto/Japan Edited by H. Araki Springer-Verlag Berlin.Heidelberg • New York 1975 Editor Prof. Huzihiro Araki Research Institute for Mathematical Sciences Kyoto University Kyoto 606/Japan Library of Congress Cataloging in Publication Data International Symposium on Mathematical Problems in Theoretical Physies, Kyoto University, 1975. Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics (M~) January 23-29, 1975, Kyoto University, Kyoto, Japan. (Lecture notes in physics ; 59) Bibliography: p. Includes index. i. Mathematieal physics--Congresses. I. Araki, Humihir o, 1952- II. Series. QCI9.2. I57 1975 550.1'5 75-17580 ISBN 3-540-07174-1 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-07174-1 Springer-Verlag New York Heidelberg Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photo- copying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin • Heidelberg 1975 Printed in Germany Offsetprinting and bookbinding: Julius Beltz, Hemsbach/Bergstr. FOREWORD This volume is the Proceedings of the International Symposium on Mathematical Problems in Theoretical Physics which was held at Research Institute for Mathematical Sciences (RIMS) and Research Institute for Fundamental Physics (RIFP) of Kyoto University, Kyoto, Japan on January 23-29, 1975. The subject of the Symposium is mainly mathematical problems in quantum field theory and statistical mechanics along with related mathematics. The Symposium was attended by both mathematicians and theoretical physicists working in different fields such as theory of elementary particles, quantum field theory, statistical mechanics, theory of probability, theory of operator algebras, theory of hyper- functions, mathematical scattering theory, linear and nonlinear differential equations. The aim of the Symposium is to provide an opportunity to find out recent results and outstanding problems in boundary areas of mathematics and physics and to promote an interaction between mathematicians and physicists. On the side of physics, attention is focussed on methods in quantum field theory and statistical mechanics and as a consequence phenomenology is not included. On the side of mathematics, attention is focussed on those areas which have lively interactions with quantum field theory and statistical mechanics. Obviously there are other areas of physics, such as fluid mechanics and general relativity, which have lively interaction with mathematics but which could not be included. This kind of international meetings of mathematical physicists was started by the International Conference on Mathematical Problems in Quantum Field Theory and Quantum Statistics held at Steklov Mathematical Institute in Moscow, USSR, on December 12-18, 1972. This Symposium is the second in the series. The symbol mark Mn ¢ adopted in both meetings denotes the intersection of mathematics and physics and well indicates the interdisciplinary character of these meetings. It is hoped that this series of international meetings of mathematical physicists continue to be held biannually or triannually. In writing contributions in this Proceedings, each speaker of the Symposium has been asked to make it suitable for Lecture Notes in Physics. A full paper with technical details is supposed to be iV published elsewhere. Review of a subject, report on recent new results, description of outstanding problems and well-defined proposal or con- jecture, along with appropriate references, are supposed to be included. Thus this volume is hopedto be useful for graduate students in finding out an appropriate subject for his research and for mathematicians and physicists in finding out what is happening in their neighbouring fields as well as in his own field. Discussions on each contribution in the SympoSium are written mostly on the spot by relevant persons and are given to the speaker. Each speaker is then given a complete freedom in deciding whether he includes a certain question or comment into "Discussion" part of his manuscripts for this Proceedings. Contributions are grouped into 30 Sessions, and arranged in the order of presentation in each Session. Each morning Session (numbered 1 to 6) includes two one-hour review talks. Afternoon Sessions, which were done in parallel 2 at a time and 4 altogether in each afternoon, are arranged with odd numbered Sessions (held at RIMS) first and even numbered Sessions (held at RIFP) afterwards in each afternoon. Other- wise Sessions are arranged in chronological order. Authors of the last two articles were unable to attend the Symposium but kindly sent in their manuscripts which they had already prepared for presentation at the Symposium. Grouping of the contributions into Sessions were originally planned according to the subject of contributions. However, due to various reasons, last minutes rearrangement of the schedule caused some mixing. In addition, some contributions are related with more than one subjects and some others do not fit well into the original classification. Therefore we delete the subject title of each Session in this Proceedings. Instead we provide a Subject Index in which a contribution may appear more than once under different subjects. The members of the Organizing Committee were as follows: Huzihiro ARAKI, Hiroshi FUJITA, Masakuni IDA, Teruo IKEBE, Kyozi KAWASAKI, Ziro MAKI, Sigeru MIZOHATA, Noboru MAKANISHI, Kazuhiko NISHIJIMA, David RUELLE, Miklo SATO, Vasilie Sergeevfch VLADIMIROV, Hisaaki YOSHIZAWA(Chairman). The Symposium was sponsored by International Mathematical Union, Japan Society for the Promotion of Science and Science Council Of Japan. We wish to thank these organizations for their financial and moral V support of the Symposium. We wish to express our appreciations and thanks to all authors of contributions in this Proceedings for their splendid works and for their co-operation with assigned page limitation and early deadline, to all participants of the Symposium and to all secretarial and administrative staffs of host Institutes for their effort in bringing this Symposium to success. March, 1975 Huzihiro ARAKI Executive Secretary of the Symposium Table of Contents Session ~ (Chairman: H. J. Borchers) D. Iagolnitzer: Analytlcity properties of scattering amplitudes: a review of some recent developments ...... l~ M. Sato: Recent development in hyperfunction theory and its application to physics. (Microlocal analysis of S-matrices and related quantities.) ....... 13\i~ Session ll (Chairman: H. Komatsu) M. Kashiwara: Micro-local calculus ................ 30~ T. Kawai and H. P. Stapp: Microlocal study of ! S-matrix singularity structure ................ 38~ M. Morimoto: Convolutors for ultrahyperfunctions ......... 4~ Session l~ (Chairman: M. Sato) \ T. Kinoshita and A. Ukawa: Mass singularities of q Feynman amplitudes ..................... .55 K. Pohlmeyer: Large momentum behaviour of Feynman amplitudes .......................... 59J G. Sommer: Spectral dependence of the analyticlty domain of local vertex functions .................. 66 Session 12 (Chairman: K. NishiJima) E. Brining and P. Stiche!: Asymptotics and light-cone singularities in quantum field theory ............ 72 S. Schlieder: Structure of singularities of Wightman- ~V distributions and the Wilson-Zimmermann-expansion respectively lightcone-expansion ............... 85\~, B. Schroer: Conformal invariance in Minkowskian quantum ~\I field theory and global operator expansions ......... 92 K. Symanzik: On some massless superrenormalizable and non-renormalizable theories ............... 102 Session ~4 (Chairman: Y. Ohnuki) Y. 0hnuki and S. Kamefuchi: The locality condition in F parafermi field theory ................... 107~ M. Ninomiya and K. Watanabe: Bound state nature and deep inelastic structure functions ................ lll V V. P. Shelest: The physical content of the statistical bootstrap and high energy hadron interaction ........ ll4 VIII K. Kinoshita: Fleld theoretical approach to composite particle reactions ..................... ll6 Session 2 (Chairman: J. R. Klauder) J. Glimm and A. Jaffe: Particles and bound states and / progress toward unitarity and scaling ........... ll8 K. Kikkawa: Field theory of relativistic strings ........ 128 S~ssion 21 (Chairman: N. Mugibayashi) / K. Hepp: Results and problems in irreversible statistical // mechanics of open systems ................. 13~ J. S. Feldman and K. Osterwalder: The Wightman axioms ~/ and the mass gap for weakly coupled (¢4) 3 quantum / field theories ....................... 151 Session 2~ (Chairman: H. Ezawa) J. R. Klauder: Soluble models and the meaning of nonrenormalizability .................... 160f Y. Kato: Bound states and asymptotic fields in model field theories ....................... 170/'~ Session 22 (Chairman: M. Ida) M. Minami: Feynman propagators associated with the Veneziano model ........... ........... 175 ! T. Yoneya: Dual string
Load more

Recommended publications
  • April 2010 Contents
    International Association of Mathematical Physics News Bulletin April 2010 Contents International Association of Mathematical Physics News Bulletin, April 2010 Contents Reflections on the IAMP Geography 3 Aharonov-Bohm & Berry Phase Anniversaries 50/25 5 The 25th anniversary of the founding of HARL 8 An interview with Huzihiro Araki 10 Shing-Tung Yau the Wolf Prize laureate 2010 in Mathematics 14 News from the IAMP Executive Committee 22 A new associated member: PIMS 26 Bulletin editor Valentin Zagrebnov Editorial board Evans Harrell, Masao Hirokawa, David Krejˇciˇr´ık, Jan Philip Solovej Contacts [email protected] http://www.iamp.org Cover photo (courtesy of Professor A.Tonomura): From double-slit experiment to the Aharonov-Bohm effect. See a comment at the end of the page 7. The views expressed in this IAMP News Bulletin are those of the authors and do not necessary represent those of the IAMP Executive Committee, Editor or Editorial board. Any complete or partial performance or reproduction made without the consent of the author or of his successors in title or assigns shall be unlawful. All reproduction rights are henceforth reserved, mention of the IAMP News Bulletin is obligatory in the reference. (Art.L.122-4 of the Code of Intellectual Property). 2 IAMP News Bulletin, April 2010 Editorial Reflections on the IAMP Geography by Pavel Exner (IAMP President) The topic of today’s meditation was inspired by complaints of American colleagues about the shaky position our discipline enjoys in the U.S. True, such woes are ubiquitous since com- petition for resources in science was and will always be tough.
    [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]
  • 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]
  • Operator Algebras and Applications, Volume 38-Part 1
    http://dx.doi.org/10.1090/pspum/038.1 PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS Volume 38, Part 1 OPERATOR ALGEBRAS AND APPLICATIONS AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND 1982 PROCEEDINGS OF THE SYMPOSIUM IN PURE MATHEMATICS OF THE AMERICAN MATHEMATICAL SOCIETY HELD AT QUEENS UNIVERSITY KINGSTON, ONTARIO JULY 14-AUGUST 2, 1980 EDITED BY RICHARD V. KADISON Prepared by the American Mathematical Society with partial support from National Science Foundation grant MCS 79-27061 Library of Congress Cataloging in Publication Data Symposium in Pure Mathematics (1980: Queens University, Kingston, Ont.) Operator algebras and applications. (Proceedings of symposia in pure mathematics; v. 38) Includes bibliographies and index. 1. Operator algebras-Congresses. I. Kadison, Richard V., 1925— II. Title. III. Series. QA326.S95 1982 512'.55 82-11561 ISBN 0-8218-1441-9 (v. 1) ISBN 0-8218-1444-3 (v. 2) ISBN 0-8218-1445-1 (set) 1980 Mathematics Subject Classification. Primary 46L05, 46L10; Secondary 43A80, 81E05, 82A15. Copyright © 1982 by the American Mathematical Society Printed in the United States of America All rights reserved except those granted to the United States Government. This book may not be reproduced in any form without the permission of the publishers. TABLE OF CONTENTS PARTI Author index xi Preface RICHARD V. KADISON xvn* Operator algebras—the first forty years 1 RICHARD V. KADISON On the structure theory of C*-algebras: some old and new problems 19 EDWARD G. EFFROS Homological invariants of extensions of C*-algebras 35 JONATHAN ROSENBERG Geometric resolutions and the Kunneth formula for C*-algebras 77 CLAUDE SCHOCHET The J£-groups for free products of C*-algebras 81 JOACHIM CUNTZ The internal structure of simple C*-algebras 85 JOACHIM CUNTZ K homology and index theory 117 PAUL BAUM AND RONALD G.
    [Show full text]
  • Is Our Mathematics Natural? the Case of Equilibrium Statistical Mechanics
    BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 19, Number 1, July 1988 IS OUR MATHEMATICS NATURAL? THE CASE OF EQUILIBRIUM STATISTICAL MECHANICS DAVID RUELLE ABSTRACT. IS human 20th-century mathematics a natural or an arbi­ trary logical construct? Some insight into this ill-posed but fascinating question is gained from the study of mathematical physics. A number of ideas introduced by physical rather than mathematical necessity turn out later to be mathematically useful. (Equilibrium statistical mechan­ ics has been a particularly rich source of such ideas.) In view of this the author argues that our mathematics may be much more arbitrary than we usually like to think. 1. Is our mathematics natural? The story goes that, when he reached heaven, Wolfgang Pauli requested to see his Creator, and asked Him to explain why the fine structure constant of electrodynamics has the value a « 1/137. The Almighty went to the blackboard, and was busy writing formulae for a couple of hours. During that time Pauli sat, shaking his head and not saying a word. When finally the answer came: a~l — 137.0359..., Pauli stood up, still shaking his head, took the chalk and pointed to an essential flaw in the calculation. I heard the story from Res Jost, and I wouldn't bet that it is completely authentic. Anyway, I think that many of us would like to ask some questions about physics and mathematics of Him who knows—when the opportunity arises. There are a number of obvious questions. For instance, about the consistency of mathematics: has He
    [Show full text]
  • Rudolf Haag's Legacy of Local Quantum Physics And
    Rudolf Haag’s legacy of Local Quantum Physics and reminiscences about a cherished teacher and friend In memory of Rudolf Haag (1922-2016) submitted to the Eur. Phys. J. H Bert Schroer permanent address: Institut f¨ur Theoretische Physik FU-Berlin, Arnimallee 14, 14195 Berlin, Germany November 2016 Abstract After some personal recollectioms about Rudolf Haag and his thoughts which led him to ”Local Quantum Physics”, the present work recalls his ideas about scattering theory, the relation between local observables and localized fields and his contributions to the physical aspects of modu- lar operator theory which paved the way for an intrisic understanding of quantum causal localization in which fields ”coordinatize” the local algebras. The paper ends with the presentation of string-local fields whose con- struction and use in a new renormalization theory for higher spin fields is part of an ongoing reformulation of gauge theory in the conceptual setting of Haag’s LQP. 1 First encounter with Rudolf Haag arXiv:1612.00003v1 [math-ph] 30 Nov 2016 On his return from the Niels Bohr Institute in Copenhagen to the University of Munich Rudolf Haag passed through Hamburg to meet his colleague Harry Lehmann, at that time the newly appointed successor of Wilhelm Lenz who held the chair of theoretical physics since the 1920 foundation of the University of Hamburg. It was the year 1958 shortly after the decision to construct the DESY particle accelerator in Hamburg which created a lot of excitement. I had nearly completed my diploma thesis under Lehmann and begun to worry about my career.
    [Show full text]
  • Current Groups and the Hamiltonian Anomaly
    CURRENTGROUPSANDTHEHAMILTONIANANOMALY ossi niemimäki Doctoral dissertation to be presented for public examination with the permission of the Faculty of Science of the University of Helsinki, in Auditorium 107, Athena Building, on the 27th of May 2020 at 14 o’clock. Department of Mathematics and Statistics Faculty of Science University of Helsinki Helsinki 2020 isbn 978-951-51-5976-2 (paperback) isbn 978-951-51-5977-9 (pdf) http://ethesis.helsinki.fi Unigraa Oy Helsinki 2020 if you’re going to try, go all the way. there is no other feeling like it. you will be alone with the gods and the nights will ame with re. — Charles Bukowski ABSTRACT Gauge symmetry invariance is an indispensable aspect of the eld-theoretic models in classical and quantum physics. Geometrically this symmetry is often modelled with current groups and current algebras, which are used to capture both the idea of gauge invariance and the algebraic structure of gauge currents related to the symmetry. The Hamiltonian anomaly is a well-known problem in the quantisation of massless fermion elds, originally manifesting as additional terms in current algebra commutators. The appearance of these anomalous terms is a signal of two things: that the gauge invariance of quantised Hamiltonian operators is broken, and that consequently it is not possible to coherently dene a vacuum state over the physical conguration space of equivalent gauge connections. In this thesis we explore the geometric and topological origins of the Hamiltonian anomaly, emphasising the usefulness of higher geometric structures in the sense of category theory. Given this context we also discuss higher versions of the gauge-theoretic current groups.
    [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]
  • Algebraic Quantum Field Theory--An Introduction
    Algebraic Quantum Field Theory – an introduction Christopher J Fewster∗1 and Kasia Rejzner†1 1Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom. November 19, 2019 Abstract We give a pedagogical introduction to algebraic quantum field theory (AQFT), with the aim of explaining its key structures and features. Topics covered include: algebraic formulations of quantum theory and the GNS representation theorem, the appearance of unitarily inequivalent representations in QFT (exemplified by the van Hove model), the main assumptions of AQFT and simple models thereof, the spectrum condition, Reeh–Schlieder theorem, split property, the universal type of local algebras, and the theory of superselection sectors. The abstract discussion is illustrated by concrete examples. One of our concerns is to explain various ways in which quantum field theory differs from quantum mechanics, not just in terms of technical detail, but in terms of physical content. The text is supplemented by exercises and appendices that enlarge on some of the relevant mathematical background. These notes are based on lectures given by CJF for the International Max Planck Research School at the Albert Einstein Institute, Golm (October, 2018) and by KR at the Raman Research Institute, Bangalore (January, 2019). Contents 1 Introduction 2 2 Algebraic quantum mechanics 4 2.1 Postulatesofquantummechanics. ....... 4 2.2 Algebraicapproach ............................... ... 5 2.3 Statesandrepresentations. ....... 7 arXiv:1904.04051v2 [hep-th] 18 Nov 2019 3 Case study: the van Hove model 10 4 Algebraic QFT 13 4.1 Basicrequirements ............................... ... 13 4.2 Examples ....................................... 15 4.3 Quasifreestatesforthefreescalarfield . ........... 20 5 The spectrum condition and Reeh–Schlieder theorem 24 5.1 Thespectrumcondition.
    [Show full text]
  • Arthur Jaffe's Publications
    Arthur Jaffe’s Publications Revised August 2020 [1] Complex Angular Momentum in Two-Channel Problems, with Y.S. Kim, Phys. Rev., 127 (1962), 2261{2266. [2] Asymptotic Behavior of the S Matrix for High Angular Momentum, with Y.S. Kim, Phys. Rev., 129 (1963), 2818{2823. [3] Divergence of Perturbation Theory for Bosons, Commun. Math. Phys., 1 (1965), 127{149. [4] Entire Functions of the Free Field, Ann. Phys. (N.Y.), 32 (1965), 127{156. [5] Nonpositivity of the Energy Density in Quantized Field Theories, with H. Epstein and V. Glaser, Nuovo Cimento, 36 (1965), 1016{1022. [6] On the Approximation of Quantum Field Theories, J. Math. Phys., 6 (1965), 1172{1178. [7] Dynamics of a Cut-off λφ4 Field Theory, Princeton University Thesis (1965). [8] Existence Theorems for a Cut-off λφ4 Field Theory, in Mathematical Theory of Elementary Particles, R. Goodman and I. Segal (eds.), MIT Press (l966). [9] Local Quantum Fields at Operator-Valued Generalized Functions, in Conference on Dispersion Theory at MIT, I.E. Segal (ed.), MIT (1966). [10] A Preliminary Study of Infinite Volume Limits in a Cut-off λφ4 Field Theory, Conference on Functional Integration and Constructive Quantum Field Theory, Editor, I.E. Segal, MIT (1966). [11] Wick Polynomials at a Fixed Time, J. Math. Phys., 7 (1966), 1250{1255. [12] Form Factors at Large Momentum Transfer, Phys. Rev. Lett., 17 (1966), 661{663. [13] High Energy Behavior of Local Quantum Fields, SLAC PUB 250 (1966), Stanford Linear Accelerator Center. [14] A Generalization of the Paley-Wiener-Schwartz Theorem, SIAM Review, 15 (1967), 1046{ 1047.
    [Show full text]
  • Notices of the American Mathematical Society
    ISSN 0002-9920 of the American Mathematical Society February 2004 Volume 51, Number 2 Geometrization of 3-Manifolds via the Ricci Flow page 184 RIMS, an Institute for Japan and the World page 194 Los Angeles Meeting page 290 Lawrenceville Meeting page 292 Houston Meeting page 295 Heawood's demonstration of Kempe's error (see page 207) Document conversion between Microsoft™ WORD and LaTeX is easier than watching PING-PONG! Paintwork © 2003 Alex Chikrii. a, rd \i Word2TeX and TeX2Word are either registered trademarks or trademarks of Chikrii Softlab in the United States and/ or other countries. Microsoft, Microsoft Word are either registered trademarks or trademarks of Microsoft Corporation in the United States and/ or other countries. Other product and company names mentioned herein may be trademarks of their respective owners. ~ Chikrii Soft lab ~ http:/jwww.chikrii.com International Mathematics Research Notices Editors Website: http://imrn.hindawi.com Morris Weisfeld IMRN provides very fast publication of research articles of high current interest in all Managing Editor areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics. Issues are published as frequently as nec­ Dan Abramovich essary. IMRN is expected to publish 80± issues in volume 2004. The articles of the IMRN are Enrico Arbarello reviewed/indexed in COMPUMATH Citation Index, Current Contents, lSI Alerting Services, Joseph Bernstein Mathematical Reviews, Science Citation Index, SciSearch, and Zentralblatt fUr Mathematik. Enrico Bombieri There are no page charges. Submissions are made by email to [email protected]. Richard E. Borcherds New print subscribers shall receive a free copy of all back volumes, i.e., volumes 1991-2003.
    [Show full text]
  • 50 Years of Communications in Mathematical Physics !
    50 Years of Communications in Mathematical Physics ! 50 Years of Communications in Mathematical Physics ! by Arthur Jaffe (Harvard) Arthur Jaffe, the Landon T. Clay Professor of Mathemat- ics and Theoretical Science at Harvard University, studied at Princeton and Cambridge Universities, starting in experimen- tal chemistry, transitioning through mathematics, and ending in mathematical physics. He has been on the faculty of Harvard University since 1967, and has served as President of the In- ternational Association of Mathematical Physics, President of the American Mathematical Society, and Chair of the Council of Scientific Society Presidents. He was a founding Member, Director, and first President of the Clay Mathematics Insti- tute. He hears the mathematical physics community speaking with one voice. This summer marks a milestone in the history of our subject: the first issue of Com- munications in Mathematical Physics appeared just fifty years ago! This remarkable initiative originated with a small group of researchers who sorely felt the need for a jour- nal that specialized in mathematical physics. Thinking back it is hard to imagine how our subject would have evolved so coherently without this top-quality, high-profile journal. A key person in the founding of CMP was Res Jost in Z¨urich. He believed in the need for a journal in which physics and mathematics were both central. Jost was a friend of Konrad Springer, heir to the family dynasty that became famous for publishing outstanding scientific books and journals. In those times, personal connections and a close camaraderie led to many good developments. Res Jost, Jr. described to me how Konrad Springer met his father in the Josts' new home in Unterengstringen (a Z¨urich suburb) to discuss the possibilities for a new journal.
    [Show full text]