Jaffe, Arthur 1937
Overview
Works:  61 works in 205 publications in 4 languages and 2,937 library holdings 

Genres:  Autobiographies Biography Conference papers and proceedings Records and correspondence Biographies History 
Roles:  Author, Editor, htt 
Classifications:  BF109.J8, 150.1954092 
Publication Timeline
.
Most widely held works about
Arthur Jaffe
 Oral history interview with Arthur M. Jaffe by Arthur Jaffe( )
 Important drawings and paintings by old masters by Sotheby's (Firm)( Book )
 Important drawings and paintings by old masters by Sotheby's (Firm)( Book )
 Jaffe, Arthur Michael : mathematical physics( )
Most widely held works by
Arthur Jaffe
Quantum physics : a functional integral point of view by
James Glimm(
Book
)
38 editions published between 1981 and 1987 in 3 languages and held by 1,024 WorldCat member libraries worldwide
Describes fifteen years' work which has led to the construc tion of solutions to nonlinear relativistic local field e quations in 2 and 3 spacetime dimensions. Gives proof of the existence theorem in 2 dimensions and describes many properties of the solutions
38 editions published between 1981 and 1987 in 3 languages and held by 1,024 WorldCat member libraries worldwide
Describes fifteen years' work which has led to the construc tion of solutions to nonlinear relativistic local field e quations in 2 and 3 spacetime dimensions. Gives proof of the existence theorem in 2 dimensions and describes many properties of the solutions
Vortices and monopoles : structure of static gauge theories by
Arthur Jaffe(
Book
)
17 editions published between 1980 and 1981 in 3 languages and held by 366 WorldCat member libraries worldwide
17 editions published between 1980 and 1981 in 3 languages and held by 366 WorldCat member libraries worldwide
The Millennium prize problems(
Book
)
9 editions published in 2006 in English and held by 315 WorldCat member libraries worldwide
"Guided by the premise that solving some of the world's most important mathematical problems will advance the field, this book offers a fascinating look at the seven unsolved Millennium Prize problems. This work takes the unprecedented approach of describing these important and difficult problems at the professional level. In announcing the seven problems and a US$7 million prize fund in 2000, the Clay Mathematics Institute emphasized that mathematics still constitutes an open frontier with important unsolved problems. The descriptions in this book serve the Institute's mission to "further the beauty, power and universality of mathematical thinking." Separate chapters are devoted to each of the seven problems: the Birch and SwinnertonDyer Conjecture, the Hodge Conjecture, the NavierStokes Equation, the P versus NP Problem, the Poincaré Conjecture, the Riemann Hypothesis, and Quantum YangMills Theory"Publisher's website
9 editions published in 2006 in English and held by 315 WorldCat member libraries worldwide
"Guided by the premise that solving some of the world's most important mathematical problems will advance the field, this book offers a fascinating look at the seven unsolved Millennium Prize problems. This work takes the unprecedented approach of describing these important and difficult problems at the professional level. In announcing the seven problems and a US$7 million prize fund in 2000, the Clay Mathematics Institute emphasized that mathematics still constitutes an open frontier with important unsolved problems. The descriptions in this book serve the Institute's mission to "further the beauty, power and universality of mathematical thinking." Separate chapters are devoted to each of the seven problems: the Birch and SwinnertonDyer Conjecture, the Hodge Conjecture, the NavierStokes Equation, the P versus NP Problem, the Poincaré Conjecture, the Riemann Hypothesis, and Quantum YangMills Theory"Publisher's website
Statistical physics and dynamical systems : rigorous results by
J Fritz(
Book
)
12 editions published in 1985 in English and held by 258 WorldCat member libraries worldwide
12 editions published in 1985 in English and held by 258 WorldCat member libraries worldwide
Quantum field theory and statistical mechanics : expositions by
James Glimm(
Book
)
16 editions published in 1985 in English and German and held by 223 WorldCat member libraries worldwide
This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. They include a solution of the original interacting quantum field equations and a description of the physics which these equations contain. Quantum fields were proposed in the late 1920s as the natural framework which combines quantum theory with relativ ity. They have survived ever since. The mathematical description for quantum theory starts with a Hilbert space H of state vectors. Quantum fields are linear operators on this space, which satisfy nonlinear wave equations of fundamental physics, including coupled Dirac, Max well and YangMills equations. The field operators are restricted to satisfy a "locality" requirement that they commute (or anticommute in the case of fer mions) at spacelike separated points. This condition is compatible with finite propagation speed, and hence with special relativity. Asymptotically, these fields converge for large time to linear fields describing free particles. Using these ideas a scattering theory had been developed, based on the existence of local quantum fields
16 editions published in 1985 in English and German and held by 223 WorldCat member libraries worldwide
This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. They include a solution of the original interacting quantum field equations and a description of the physics which these equations contain. Quantum fields were proposed in the late 1920s as the natural framework which combines quantum theory with relativ ity. They have survived ever since. The mathematical description for quantum theory starts with a Hilbert space H of state vectors. Quantum fields are linear operators on this space, which satisfy nonlinear wave equations of fundamental physics, including coupled Dirac, Max well and YangMills equations. The field operators are restricted to satisfy a "locality" requirement that they commute (or anticommute in the case of fer mions) at spacelike separated points. This condition is compatible with finite propagation speed, and hence with special relativity. Asymptotically, these fields converge for large time to linear fields describing free particles. Using these ideas a scattering theory had been developed, based on the existence of local quantum fields
Quantum field theory : a selection of papers in memorian Kurt Symanzik by
Arthur Jaffe(
Book
)
7 editions published in 1985 in English and Italian and held by 128 WorldCat member libraries worldwide
Kurt Symanzik was certainly one of the most outstanding theoretical physicists of our time. For thirty years, until his untimely death in 1983, he helped to shape the present form of quantum field theory and its application to elementary particle physics. In memoriam of Kurt" Symanzik leading scientists present their most recent results, giving, at the same time, an overview of the state of the art. This collection was originally published in Vol. 97, 1/2 (1985) of Communications in Mathematical Physics. They range over various inter related topics of interest to Kurt Symanzik. We hope that making this collection available in an accessible and inexpensive way will benefit the physics community. The Publisher Contents To the Memory of Kurt Symanzik 1 By A. Jaffe, H. Lehmann, and G. Mack Monte Carlo Simulations for Quantum Field Theories Involving Fermions. By M. Karowski, R. Schrader, and H. J. Thun (With 8 Figures) . . . . . . . . . . . . . . . . . . . 5 SU(2) Lattice Gauge Theory: Standard Action Versus Symanzik's TreeImproved Action. By B. Berg, A. Billoire, S. Meyer, and C. Panagiotakopoulos (With 13 Figures). . . . . . . . . . 31 . Onshell Improved Lattice Gauge Theories By M. Luscher and P. Weisz (With 3 Figures) . . . . . 59 On the Modular Structure of Local Algebras of Observables By K. Fredenhagen . . . . . . . . . . . . . . . . . 79 . . . The Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory By M. Aizenman (With 3 Figures). . . . . . . . . . . . 91 Intersection Properties of Simple Random Walks: A Renormalization Group Approach. By G. Felder and J. Frohlich. . . . . . . 111
7 editions published in 1985 in English and Italian and held by 128 WorldCat member libraries worldwide
Kurt Symanzik was certainly one of the most outstanding theoretical physicists of our time. For thirty years, until his untimely death in 1983, he helped to shape the present form of quantum field theory and its application to elementary particle physics. In memoriam of Kurt" Symanzik leading scientists present their most recent results, giving, at the same time, an overview of the state of the art. This collection was originally published in Vol. 97, 1/2 (1985) of Communications in Mathematical Physics. They range over various inter related topics of interest to Kurt Symanzik. We hope that making this collection available in an accessible and inexpensive way will benefit the physics community. The Publisher Contents To the Memory of Kurt Symanzik 1 By A. Jaffe, H. Lehmann, and G. Mack Monte Carlo Simulations for Quantum Field Theories Involving Fermions. By M. Karowski, R. Schrader, and H. J. Thun (With 8 Figures) . . . . . . . . . . . . . . . . . . . 5 SU(2) Lattice Gauge Theory: Standard Action Versus Symanzik's TreeImproved Action. By B. Berg, A. Billoire, S. Meyer, and C. Panagiotakopoulos (With 13 Figures). . . . . . . . . . 31 . Onshell Improved Lattice Gauge Theories By M. Luscher and P. Weisz (With 3 Figures) . . . . . 59 On the Modular Structure of Local Algebras of Observables By K. Fredenhagen . . . . . . . . . . . . . . . . . 79 . . . The Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory By M. Aizenman (With 3 Figures). . . . . . . . . . . . 91 Intersection Properties of Simple Random Walks: A Renormalization Group Approach. By G. Felder and J. Frohlich. . . . . . . 111
Collected papers by
James Glimm(
Book
)
10 editions published between 1984 and 1985 in English and held by 109 WorldCat member libraries worldwide
10 editions published between 1984 and 1985 in English and held by 109 WorldCat member libraries worldwide
Constructive quantum field theory : selected papers by
James Glimm(
Book
)
4 editions published in 1985 in English and held by 68 WorldCat member libraries worldwide
4 editions published in 1985 in English and held by 68 WorldCat member libraries worldwide
Progress in gauge field theory by
G 't Hooft(
)
2 editions published between 1983 and 1984 in English and held by 53 WorldCat member libraries worldwide
The importance of gauge theory for elementary particle physics is by now firmly established. Recent experiments have yielded con vincing evidence for the existence of intermediate bosons, the carriers of the electroweak gauge force, as well as for the presence of gluons, the carriers of the strong gauge force, in hadronic inter actions. For the gauge theory of strong interactions, however, a number of important theoretical problems remain to be definitely resolved. They include the quark confinement problem, the quantita tive study of the hadron mass spectrum as well as the role of topo logy in quantum gauge field theory. These problems require for their solution the development and application of nonperturbative methods in quantum gauge field theory. These problems, and their nonpertur bative analysis, formed the central interest of the 1983 Cargese summer institute on "Progress in Gauge Field Theory." In this sense it was a natural sequel to the 1919 Cargese summer institute on "Recent Developments in Gauge Theories." Lattice gauge theory provides a systematic framework for the investigation of nonperturbative quantum effects. Accordingly, a large number of lectures dealt with lattice gauge theory. Following a systematic introduction to the subject, the renormalization group method was developed both as a rigorous tool for fundamental questions, and in the blockspin formulation, the computations by Monte Carlo programs. A detailed analysis was presented of the problems encountered in computer simulations. Results obtained by this method on the mass spectrum were reviewed
2 editions published between 1983 and 1984 in English and held by 53 WorldCat member libraries worldwide
The importance of gauge theory for elementary particle physics is by now firmly established. Recent experiments have yielded con vincing evidence for the existence of intermediate bosons, the carriers of the electroweak gauge force, as well as for the presence of gluons, the carriers of the strong gauge force, in hadronic inter actions. For the gauge theory of strong interactions, however, a number of important theoretical problems remain to be definitely resolved. They include the quark confinement problem, the quantita tive study of the hadron mass spectrum as well as the role of topo logy in quantum gauge field theory. These problems require for their solution the development and application of nonperturbative methods in quantum gauge field theory. These problems, and their nonpertur bative analysis, formed the central interest of the 1983 Cargese summer institute on "Progress in Gauge Field Theory." In this sense it was a natural sequel to the 1919 Cargese summer institute on "Recent Developments in Gauge Theories." Lattice gauge theory provides a systematic framework for the investigation of nonperturbative quantum effects. Accordingly, a large number of lectures dealt with lattice gauge theory. Following a systematic introduction to the subject, the renormalization group method was developed both as a rigorous tool for fundamental questions, and in the blockspin formulation, the computations by Monte Carlo programs. A detailed analysis was presented of the problems encountered in computer simulations. Results obtained by this method on the mass spectrum were reviewed
Recent developments in gauge theories by
G.'t Hooft(
)
4 editions published in 1980 in English and held by 51 WorldCat member libraries worldwide
Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gauge theory of weak and electromagnetic interactions, and finally to a non abelian gauge theory of strong interactions with the notion of permanently confined quarks. The. early theoretical work on gauge theories was devoted to proofs of renormalizability, investigation of short distance behaviour, the discovery of asymptotic freedom, etc . . , aspects which were accessible to tools extrapolated from renormalised perturbation theory. The second phase of the subject is concerned with the problem of quark confinement which necessitates a nonperturbative understanding of gauge theories. This phase has so far been marked by the introduc tion of ideas from geometry, topology and statistical mechanics in particular the theory of phase transitions. The 1979 Cargese Institute on "Recent Developments on Gauge Theories" was devoted to a thorough discussion of these nonperturbative, global aspects of nonabelian gauge theories. In the lectures and seminars reproduced in this volume the reader wilf find detailed reports on most of the important developments of recent times on non perturbative gauge fields by some of the leading experts and innovators in this field. Aside from lectures on gauge fields proper, there were lectures on gauge field concepts in condensed matter physics and lectures by mathematicians on global aspects of the calculus of variations, its relation to geometry and topology, and related topics
4 editions published in 1980 in English and held by 51 WorldCat member libraries worldwide
Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gauge theory of weak and electromagnetic interactions, and finally to a non abelian gauge theory of strong interactions with the notion of permanently confined quarks. The. early theoretical work on gauge theories was devoted to proofs of renormalizability, investigation of short distance behaviour, the discovery of asymptotic freedom, etc . . , aspects which were accessible to tools extrapolated from renormalised perturbation theory. The second phase of the subject is concerned with the problem of quark confinement which necessitates a nonperturbative understanding of gauge theories. This phase has so far been marked by the introduc tion of ideas from geometry, topology and statistical mechanics in particular the theory of phase transitions. The 1979 Cargese Institute on "Recent Developments on Gauge Theories" was devoted to a thorough discussion of these nonperturbative, global aspects of nonabelian gauge theories. In the lectures and seminars reproduced in this volume the reader wilf find detailed reports on most of the important developments of recent times on non perturbative gauge fields by some of the leading experts and innovators in this field. Aside from lectures on gauge fields proper, there were lectures on gauge field concepts in condensed matter physics and lectures by mathematicians on global aspects of the calculus of variations, its relation to geometry and topology, and related topics
Nonperturbative quantum field theory by
G Hooft(
)
4 editions published between 1988 and 1989 in English and held by 48 WorldCat member libraries worldwide
During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of indext. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail
4 editions published between 1988 and 1989 in English and held by 48 WorldCat member libraries worldwide
During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of indext. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail
New Symmetry Principles in Quantum Field Theory by
J Fröhlich(
)
1 edition published in 1992 in English and held by 47 WorldCat member libraries worldwide
Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed
1 edition published in 1992 in English and held by 47 WorldCat member libraries worldwide
Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed
Probability applied to physics by
James Glimm(
Book
)
3 editions published in 1978 in English and held by 45 WorldCat member libraries worldwide
3 editions published in 1978 in English and held by 45 WorldCat member libraries worldwide
Collected papers by
James Glimm(
Book
)
8 editions published in 1985 in English and Undetermined and held by 34 WorldCat member libraries worldwide
8 editions published in 1985 in English and Undetermined and held by 34 WorldCat member libraries worldwide
Collected papers by
James Glimm(
Book
)
6 editions published in 1985 in English and Undetermined and held by 24 WorldCat member libraries worldwide
6 editions published in 1985 in English and Undetermined and held by 24 WorldCat member libraries worldwide
Current developments in mathematics, 1996(
Book
)
2 editions published in 1997 in English and held by 24 WorldCat member libraries worldwide
2 editions published in 1997 in English and held by 24 WorldCat member libraries worldwide
Letters, Vol. 1 : 19061950 by
C. G Jung(
Book
)
1 edition published in 1973 in English and held by 19 WorldCat member libraries worldwide
1 edition published in 1973 in English and held by 19 WorldCat member libraries worldwide
Memories, dreams, reflections by
Carl Gustav Jung(
Book
)
3 editions published between 1973 and 1994 in Dutch and English and held by 11 WorldCat member libraries worldwide
The autobiography of Carl Jung
3 editions published between 1973 and 1994 in Dutch and English and held by 11 WorldCat member libraries worldwide
The autobiography of Carl Jung
Collected papers by
James Glimm(
Book
)
6 editions published in 1985 in English and Undetermined and held by 9 WorldCat member libraries worldwide
6 editions published in 1985 in English and Undetermined and held by 9 WorldCat member libraries worldwide
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Related Identities
 Glimm, James Author
 Taubes, Clifford 1954
 Wiles, Andrew Editor
 Carlson, James A. 1946 Editor
 Clay Mathematics Institute Publisher Editor
 American Mathematical Society Publisher Editor
 Fritz, J. Author Editor
 Szász, D. Editor
 Stora, R. Editor
 Mitter, P. K. Editor
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Associated Subjects
ArtPrivate collections Canada Clarke, J. S.(John S.) College teachers Conscience Critical phenomena (Physics) Dreams Field theory (Physics) Gauge fields (Physics) Geometry, Differential Germany Harmonic analysis India Jaffe, Arthur, Jung, C. G.(Carl Gustav), Lie algebras Magnetic monopoles Mathematical physics Mathematics MathematicsAwards MathematicsResearch Memory Numerical analysis Phase transformations (Statistical physics) Philosophy Physicists Physics Prizes (Property captured at sea) Probabilities Psychoanalysis Psychoanalysts Psychologists Psychology Psychotherapy Quantum field theory Quantum theory Random fields Recollection (Psychology) Reflection (Philosophy) Science Scientists Sepoy Rebellion (India : 18571858) Statistical mechanics Statistical physics Switzerland Symanzik, Kurt Symmetry (Physics) Topology United States Universities and collegesFaculty
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Alternative Names
Arthur Jaffe Amerikaans wiskundige
Arthur Jaffe amerikansk fysiker och matematiker
Arthur Jaffe amerikansk fysiker og matematiker
Arthur Jaffe USamerikanischer mathematischer Physiker
Arthur Michael Jaffe
Džaffe, A.
Jaffe, A.
Jaffe, A. 1937
Jaffe, A. (Arthur), 1937
Jaffe, A. M.
Jaffe, Arthur
Jaffe, Arthur M.
Jaffe, Arthur M. 1937
Jaffe, Arthur Michael
Jaffe, Arthur Michael 1937
Артур Джаффе
آرثر جافي
아서 재피
アーサー・ジャッフェ
亚瑟·贾菲
阿瑟·贾菲
Languages