DOCSLIB.ORG

Princeton Series in Physics Edited Byphilip W.Anderson, Arthur S

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Princeton Series in Physics Edited Byphilip W.Anderson, Arthur S Princeton Series in Physics Edited byPhilip W.Anderson, Arthur S. Wlghtman, and Sam B. Trelman Quantum Mechanics for Flamiltonians Defined as Quadratic Forms byBarry Simon Lectureson Current Algebra and Its Applications bySam B. Trelman. Roman Jackiw, and David). Gross PhysicalCosmology byPIE. Peebles TheMany-Worlds Interpretation of Quantum Mechanics editedby B. S. DeWitt and N. Graham HomogeneousRelativistic Cosmologies by MichaelP. Ryan. Jr. • and Lawrence C. Shepley TheP(4), Euclidean (Quantum) Field Theory byBarry Simon Studiesin Mathematical Physics: Essays in Honor of Valentine Bargmann editedby Elliott H. Lieb, B. Simon. and A. S. Wightman Convexityin the Theory of Lattice Oases byRobert B. Israel Workson the Foundations of Statistical Physics byN. S. Krylov Surprisesin Theoretical Physics byRudolf Peierls TheLarge-Scale Structure or the Universe byPiE. Peebles StatisticalPhysics and the Atomic Theory of Matter. From Boyle and Newton to Landau and Onsager byStephen G. Brush QuantumTheory and Measurement editedby John Archibald Wheeler and Wajcierh Hubert Zurek CurrentAlgebra and Anomalies bSam B. Treiman. Roman Jackiw. Bruno Zamino. and Edward Witten Quantumfluctuations byE. Nelson SpinOlasses and Other Frustrated Systems byDebashish Chowdhury (Spin Glasses and Other Frustrated Systems ispublished in co-operation with World Scientifte Publishing Co. Pte. Ltd., Singapore.) Large-Scale Motions in the Universe: A Vatican Study Week editedby Vera C. Rabin and George V. Coyne. S.). Instabilitiesand Fronts in Extended Systems byPierre Collet and Jean-Pierre Lckmann FromPerturbative to Constructive Renormalization byVincent Rtvasseau Maxwell'sDemon: Entropy. Information. Computing editedby haney S. Leff and Andrew F. Rex MoreSurprises in Theoretical Physics byRudolf PeierLs Supcrsymmetryand Supergravity. Second Edition. Revised and Expanded by Jul:u.sWess and Jonathan Bagger Introductionto Algebraic and Constructive Quantum Field Theory /n JohnC'.Rae:. Irving E. Segal. and ZhengJang Zhou Introduction to Algebraic and Constructive Quantum Field Theory JOHN C. BAEZ IRVING E. SEGAL ZHENGFANG ZHOU PRINCETON UNIVERSITY PRESS PRINCETON.NEW JERSEY Copyright © 1992 by Princeton University Press Publishedby PrincetonUniversity Press, 41 William Street, Princeton, New Jersey 08540 Inthe United Kingdom: Princeton University Press, Oxford All Rights Reserved Library of Congress Cataloging-in-Publication Data Baez,JohnC.,1961- Introductionto algebraic and constructive quantum field theory I byJohn C. Baez, irving E. Segal, Zhengfang Zhou. p. cm. —(Princetonseries in physics) Includes bibliographical references and index. ISBN 0-691-08546-3 I. Quantum field theory. 2. I. Segal, Irving Ezra. 11. Thou, Zhengfang, 1959- .ill.Title. IV. Series. QC174.45.B291991 530.1'43—dc2O 91-16504 C1P This book has been composed in Linotron Times Roman Princeton University Press books are printed on acid-free paper, and meet the guidelines for permanence and durability of the Committee on Production Guidelines for Book Longevity of the Council on Library Resources Printed in the United States of America by Princeton University Press, Princeton, New Jersey 10 9 8 7 6 5 4 3 2 1 Designedby Laury A. Egan Contents Preface ix Introduction xiii 1. The Free Boson Field 3 1.1.introduction 3 1.2.Weyl and Heisenberg systems 4 1.3.Functional integration 15 1.4.Quasi-invariant distributions 25 1.5. Absolute continuity 30 1.6.Irreducibility and ergodicity 37 1.7.The Fourier-Wiener transform 41 1.8.The structure of r and wave-particle duality 47 1.9.Implications of wave-particle duality 57 1.10. Characterization of the free boson field 62 1.11. The complex wave representation 64 1.12. Analytic features of the complex wave representation 70 2. The Free Fermion Field 75 2.1.Clifford systems 75 2.2.Existence of the free fermion field 80 2.3.The real wave representation 82 2.4.The complex wave representation 89 3. Properties of the Free Fields 96 3.1.Introduction 96 3.2.The exponential laws 97 3.3.Irreducibility 99 3.4.Representation of the orthogonal group by measure- preserving transformations 100 Contents 3.5. Bosonic quantization of symplectic dynamics 105 3.6. Fermionic quantization of orthogonal dynamics 113 4. AbsoluteContinuityand Unitary Implementabllity 118 4.1.Introduction 118 4.2.Equivalence of distributions 119 4.3.Quasi-invariant distributions and Weyl systems 121 4.4.Ergodicity and irreducibility of Weyl pairs 124 4.5.infinite products of Hubert spaces 125 4.6.Afflne transforms of the isonormal distribution 130 4.7.Implementability of orthogonal transformations on the fermion field 135 5. Quantizatlon 142 5.1.introduction 142 5.2.Weyl algebras over a linear sympleclic space 143 5.3.Regular states of the general boson field 147 5.4.The representation-independent Clifford algebra 149 5.5.Lexicon: The distribution of occupation numbers 150 6. Quantization of Linear Differential Equations 153 6.1.lntroduction 153 6.2.The Schrödingcrequation 154 6.3.Quantization of second-order equations 158 6.4.Finite propagation velocity 160 6.5.Quantization of the Dirac equation 162 6.6.Quantization of global spaces of wave functions 168 7. Renormalized Products of Quantum Fields 174 7.1.The algebra of additive renormalization 174 7.2.Renormalized products of' the free boson field 184 7.3.Regularity properties of boson field operators 190 7.4.Renormalized local products of field operators 200 Contents 8. ConstructIon of Nonlinear Quantized Fields 208 8.1. Introduction 208 8.2.The 210 8.3.Renormalized products at fixed time 214 8.4.Properties of fixed-time renormalization 223 8.5.The semigroup generated by the interaction Hamiltonian 227 8.6.The pseudo-interacting field 229 8.7.Dynamic causality 233 8.8.The local quantized equation of motion 237 Appendix A Principal Notations 251 Appendix B Universal Fields and the Quantization of Wave EquatIons 254 Glossary 258 Bibliography 281 Index 289 Preface This book is an amplified and updated version of a graduate course given by one of us (lEs)atvarious times during the past two decades. Ills intended as a rigorous treatment from first principles of the algebraic and analytic core of general quantum field theory. The first half of the book develops the alge- braictheorycentering around boson and fermion fields, their particle and wave representations, considerations of unitary implementability. and the represen- tation-independent formalism. This is tied in with the infinite- dimensional unitary, symplectic, and orthogonal groups, and their actions as canonical transformations on corresponding types of fields, in part, this rep- resents a natural extension of harmonic analysis and aspects of the theory of classical Lie groups from the finite to the infinite-dimensional case. But certain features that are crucial in the physical context—stability(positivityof the energy or of particle numbers) and causality (finiteness of propagation veloc- ity), both of which play essential roles in the quantization of wave equations— are also central in our treatment. These features are integrated with symmetry considerations in a coherent way that defines the essence of algebraic quantum field theory and subsumes the quantization of linear wave equations of a quite general type. But the key process that distinguishes quantum from classicalphysicsis that of particleproduction. Themathematical description of this phenomenon in accordance with the physical desiderata underlined above is, at the funda- mental level, by quantized nonlinearwaveequations. The algebraic theory developed in the first part of the book is used extensively in the second part in developing the mathematical interpretation, and solution in a prototypical Coil- text,of such equations. New analytic, rather than algebraic, issues of rcnor- malization and singular perturbation arise in this connection. In particular, nonlinear local functions of quantum fields—such as fields that are not neces- sarily free, or defined over arbitrary Riemannian manifolds—are treated in general contexts. These are in the direction of ultimate extension to physically more realistic cases than the model treated here. This consists of the formula- tion of the concept of solution of a quantized local nonlinear scalar wave equa- tion in a sense that is independent of the existence of an associated free held. and of the establishment of such solutions in two space-time dimensions (al- beit by a technique that starts from a free field). This book is intended as a self-contained introduction, and not as a treatise or compendium of results. A logically coherent and detailed treatment of a x Preface subject as indivisible and multifaceted as quantum field theory must be highly selective. We eschew both "practical" and the now classical "axiomatic" quantum field theory, on which there are excellent textbooks. Those in axio- matic theory include the authoritative texts by Bogolioubov, Logunov, and Todorov (1975); Jost (1965); and Streater and Wightman (1964). The pleni- tude of texts on practical theory includes the lucid treatments, in order of in- creasing scope, of Mandl (1959); Bjorken and Drell (1965); and Cheng and Li (1984). We also fail to do justice to the geometrical side of the theory, partly be- cause to do so would require another volume of the present size, but also because our approach is designed to apply in essence to virtually arbitrary geometries, the particularities of which need not be specified. Applications and illustrations are usually given in terms of Minkowski space, because this is
Load more

Recommended publications
  • Roman Jackiw: a Beacon in a Golden Period of Theoretical Physics
    Roman Jackiw: A Beacon in a Golden Period of Theoretical Physics Luc Vinet Centre de Recherches Math´ematiques, Universit´ede Montr´eal, Montr´eal, QC, Canada [email protected] April 29, 2020 Abstract This text offers reminiscences of my personal interactions with Roman Jackiw as a way of looking back at the very fertile period in theoretical physics in the last quarter of the 20th century. To Roman: a bouquet of recollections as an expression of friendship. 1 Introduction I owe much to Roman Jackiw: my postdoctoral fellowship at MIT under his supervision has shaped my scientific life and becoming friend with him and So Young Pi has been a privilege. Looking back at the last decades of the past century gives a sense without undue nostalgia, I think, that those were wonderful years for Theoretical Physics, years that have witnessed the preeminence of gauge field theories, deep interactions with modern geometry and topology, the overwhelming revival of string theory and remarkably fruitful interactions between particle and condensed matter physics as well as cosmology. Roman was a main actor in these developments and to be at his side and benefit from his guidance and insights at that time was most fortunate. Owing to his leadership and immense scholarship, also because he is a great mentor, Roman has always been surrounded by many and has thus arXiv:2004.13191v1 [physics.hist-ph] 27 Apr 2020 generated a splendid network of friends and colleagues. Sometimes, with my own students, I reminisce about how it was in those days; I believe it is useful to keep a memory of the way some important ideas shaped up and were relayed.
    [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]
  • Reflections on a Revolution John Iliopoulos, Reply by Sheldon Lee Glashow
    INFERENCE / Vol. 5, No. 3 Reflections on a Revolution John Iliopoulos, reply by Sheldon Lee Glashow In response to “The Yang–Mills Model” (Vol. 5, No. 2). Internal Symmetries As Glashow points out, particle physicists distinguish To the editors: between space-time and internal symmetry transforma- tions. The first change the point of space and time, leaving Gauge theories brought about a profound revolution in the the fundamental equations unchanged. The second do not way physicists think about the fundamental forces. It is this affect the space-time point but transform the dynamic vari- revolution that is the subject of Sheldon Glashow’s essay. ables among themselves. This fundamentally new concept Gauge theories, such as the Yang–Mills model, use two was introduced by Werner Heisenberg in 1932, the year mathematical concepts: group theory, which is the natural the neutron was discovered, but the real history is more language to describe the physical property of symmetry, complicated.3 Heisenberg’s 1932 papers are an incredible and differential geometry, which connects in a subtle way mixture of the old and the new. For many people at that symmetry and dynamics. time, the neutron was a new bound state of a proton and Although there exist several books, and many more an electron, like a small hydrogen atom. Heisenberg does articles, relating historical aspects of these theories,1 a not reject this idea. Although for his work he considers real history has not yet been written. It may be too early. the neutron as a spin one-half Dirac fermion, something When a future historian undertakes this task, Glashow’s incompatible with a proton–electron bound state, he notes precise, documented, and authoritative essay will prove that “under suitable circumstances [the neutron] can invaluable.
    [Show full text]
  • VALENTINE BARGMANN April 6, 1908–July 20, 1989
    NATIONAL ACADEMY OF SCIENCES V ALENTINE BAR G MANN 1908—1989 A Biographical Memoir by JO H N R. KLAUDER Any opinions expressed in this memoir are those of the author(s) and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 1999 NATIONAL ACADEMIES PRESS WASHINGTON D.C. Courtesy of Princeton University Libraries, Princeton, N.J. VALENTINE BARGMANN April 6, 1908–July 20, 1989 BY JOHN R. KLAUDER ET’S ASK BARGMANN!” With that phrase—addressed to “Lme by my Princeton thesis advisor—I was led to my first real encounter with Valentine Bargmann. Our ques- tion pertained to a mathematical fine point dealing with quantum mechanical Hamiltonians expressed as differen- tial operators, and we got a prompt, clear, and definitive answer. Valya—the common nickname for Valentine Bargmann—was already an established and justly renowned mathematical physicist in the best sense of the term, and his advice was widely sought by beginners and experts alike. It was, of course, a thorough preparation that brought Valya to his well-deserved reputation. Valya Bargmann was born on April 6, 1908, in Berlin, and studied at the University of Berlin from 1925 to 1933. As National Socialism began to grow in Germany, he moved to Switzerland, where he received his Ph.D. in physics at the University of Zürich under the guidance of Gregor Wentzel. Soon thereafter he emigrated to the United States. It is noteworthy that his passport, which would have been revoked in Germany at that time, had but two days left to its validity when he was accepted for immigration into the United States.
    [Show full text]
  • 2017 Breakthrough Prizes in Mathematics and Fundamental
    COMMUNICATION 2017 Breakthrough Prizes Awarded Jean Bourgain Joseph Polchinski Andrew Strominger Cumrun Vafa Breakthrough Prize in Mathematics be obtained from the results of Weil and Deligne on the Jean Bourgain of the Institute for Advanced Study, Riemann hypothesis over finite fields), as well as the de- Princeton, New Jersey, has been selected as the recipient velopment (with Gamburd and Sarnak) of the affine sieve of the 2017 Breakthrough Prize in Mathematics by the that has proven to be a powerful tool for analyzing thin Breakthrough Prize Foundation. Bourgain was honored for groups. Most recently, with Demeter and Guth, Bourgain “major contributions across an incredibly diverse range of has established several important decoupling theorems areas, including harmonic analysis, functional analysis, er- in Fourier analysis that have had applications to partial godic theory, partial differential equations, mathematical differential equations, combinatorial incidence geometry, physics, combinatorics, and theoretical computer science.” and analytic number theory, in particular solving the Main The prize carries a cash award of US$3 million. Conjecture of Vinogradov, as well as obtaining new bounds The Notices asked Terence Tao of the University of Cal- on the Riemann zeta function.” ifornia Los Angeles to comment on the work of Bourgain (Tao was on the Breakthrough Prize committee and was Biographical Sketch: Jean Bourgain also one of the nominators of Bourgain). Tao responded: Jean Bourgain was born in 1954 in Oostende, Belgium. He “Jean Bourgain is an unparalleled problem-solver in anal- received his PhD (1977) and his habilitation (1979) from ysis who has revolutionized many areas of the subject by the Free University of Brussels.
    [Show full text]
  • What Comes Beyond the Standard Models Bled, July 11–19, 2016
    i i “proc16” — 2016/12/12 — 10:17 — page I — #1 i i BLEJSKE DELAVNICE IZ FIZIKE LETNIK 17, STˇ . 2 BLED WORKSHOPS IN PHYSICS VOL. 17, NO. 2 ISSN 1580-4992 Proceedings to the 19th Workshop What Comes Beyond the Standard Models Bled, July 11–19, 2016 Edited by Norma Susana MankoˇcBorˇstnik Holger Bech Nielsen Dragan Lukman DMFA – ZALOZNIˇ STVOˇ LJUBLJANA, DECEMBER 2016 i i i i i i “proc16” — 2016/12/12 — 10:17 — page II — #2 i i The 19th Workshop What Comes Beyond the Standard Models, 11.– 19. July 2016, Bled was organized by Society of Mathematicians, Physicists and Astronomers of Slovenia and sponsored by Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana Society of Mathematicians, Physicists and Astronomers of Slovenia Beyond Semiconductor (MatjaˇzBreskvar) Scientific Committee John Ellis, CERN Roman Jackiw, MIT Masao Ninomiya, Okayama Institute for Quantum Physics Organizing Committee Norma Susana MankoˇcBorˇstnik Holger Bech Nielsen Maxim Yu. Khlopov The Members of the Organizing Committee of the International Workshop “What Comes Beyond the Standard Models”, Bled, Slovenia, state that the articles published in the Proceedings to the 19th Workshop “What Comes Beyond the Standard Models”, Bled, Slovenia are refereed at the Workshop in intense in-depth discussions. i i i i i i “proc16” — 2016/12/12 — 10:17 — page III — #3 i i Workshops organized at Bled . What Comes Beyond the Standard Models (June 29–July 9, 1998), Vol. 0 (1999) No. 1 (July 22–31, 1999) (July 17–31, 2000) (July 16–28, 2001), Vol. 2 (2001) No. 2 (July 14–25, 2002), Vol.
    [Show full text]
  • Theoretical and Mathematical Physics New Books and Highlights in 2020/2021
    Now available on WorldSciNet Theoretical and Mathematical Physics New Books and Highlights in 2020/2021 Textbook Textbook Textbook Mathematical Methods of Theoretical Physics Roman Jackiw by Karl Svozil (Technische Universität Wien, Austria) 80th Birthday Festschrift edited by Antti Niemi (University of Stockholm, Sweden), This book contains very detailed proofs and demonstrations of common Terry Tomboulis (University of California, Los Angeles, USA) & mathematical methods used in theoretical physics. It combines and unifies Kok Khoo Phua (Nanyang Technological University, Singapore) many expositions of the subject and thus is accessible to a very wide range of students, such as those interested in experimental and applied physics. The ○ Dedicated to Roman Jackiw, a theoretical physicist known for content is divided into three parts: linear vector spaces, functional analysis his fundamental contributions in high energy physics, gravita- and differential equations. tion, condensed matter and the physics of fluids. ○ With contributions from prominent scientists including two No- 332pp Mar 2020 bel laureates and one Field Medalist. 978-981-120-840-9 US$78 £70 ○ Also included are personal recollections and humorous anec- dotes from Jackiw’s friends and colleagues. Lectures on Quantum Field Theory 336pp Aug 2020 (2nd Edition) 978-981-121-066-2 US$118 £105 by Ashok Das (University of Rochester, USA) “Comprehensive yet at the beginner’s level, lucid and informal, this new An Introduction to Inverse Problems in Physics edition of Lectures on Quantum Field Theory contains new material by M Razavy (University of Alberta, Canada) including two new chapters and two additional appendices. The book This book is a compilation of different methods of formulating and solving will be of interest to students of mathematics and theoretical physics, inverse problems in physics from classical mechanics to the potentials and teachers and researchers.” nucleus-nucleus scattering.
    [Show full text]
  • Conceptual Foundations of Quantum Field Theory Quantum Field Theory Is a Powerful Language for the Description of The
    Conceptual foundations of quantum ®eld theory Quantum ®eld theory is a powerful language for the description of the sub- atomic constituents of the physical world and the laws and principles that govern them. This book contains up-to-date in-depth analyses, by a group of eminent physicists and philosophers of science, of our present understanding of its conceptual foundations, of the reasons why this understanding has to be revised so that the theory can go further, and of possible directions in which revisions may be promising and productive. These analyses will be of interest to students of physics who want to know about the foundational problems of their subject. The book will also be of interest to professional philosophers, historians and sociologists of science. It contains much material for metaphysical and methodological re¯ection on the subject; it will also repay historical and cultural analyses of the theories discussed in the book, and sociological analyses of the way in which various factors contribute to the way the foundations are revised. The authors also re¯ect on the tension between physicists on the one hand and philosophers and historians of science on the other, when revision of the foundations becomes an urgent item on the agenda. This work will be of value to graduate students and research workers in theoretical physics, and in the history, philosophy and sociology of science, who have an interest in the conceptual foundations of quantum ®eld theory. For Bob and Sam Conceptual foundations of quantum ®eld theory EDITOR TIAN YU CAO Boston University PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge CB2 1RP, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge CB2 2RU, UK http://www.cup.cam.ac.uk 40 West 20th Street, New York, NY 10011-4211, USA http://www.cup.org 10 Stamford Road, Oakleigh, Melbourne 3166, Australia # Cambridge University Press 1999 This book is in copyright.
    [Show full text]
  • Swarthmore College Bulletin (June 1997)
    SSWWAARRTTHHMMOORREE College Bulletin June 1997 The Future of Dying Tom Preston ’55 on physician- assisted suicide Eugene M. Lang ’38, shown here surrounded by some of the current Lang Opportunity Scholars, has pledged $30 million to Swarthmore, the largest gift in College history and among the most generous ever given to a liberal arts college. Lang came to the campus in April E E L to meet prospective Lang G N E J - G Scholars for the Class of N E D 2001. For more on Eugene Lang’s “Fund for the Future,” please turn to page 6. SWARTHMORE COLLEGE BULLETIN • JUNE 1997 10 The New Face of Honors The Honors Program had fallen on hard times when the faculty voted sweeping reforms in 1994. Now enrollment is up, and students are enjoying new flexibility in preparing for external exams. Take a look at what’s happened to the College’s signa- ture program through the eyes of faculty members and students. Editor: Jeffrey Lott D Associate Editor: Nancy Lehman ’87 16 Elegant Euclid News Editor: Kate Downing Former math hater Nick Jackiw ’88 invented one of the most Class Notes Editor: Carol Brévart F widely used software programs in mathematics education, Desktop Publishing: Audree Penner R Geometer’s Sketchpad. With it two 16-year-olds created a novel T Designer: Bob Wood solution to a problem first posed by Euclid 2,300 years ago. Editor Emerita: Maralyn Orbison Gillespie ’49 A P6 P4 P2 By Eric Rich Associate Vice President for External Affairs: Barbara Haddad Ryan ’59 20 The Future of Dying Cover: Physician and Supreme Modern medicine has changed the nature of dying, argues Court plaintiff Thomas Preston ’55.
    [Show full text]
  • Hans Bethe, My Teacher
    Hans Bethe, My Teacher The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Jackiw, Roman. “Hans Bethe, My Teacher.” Physics in Perspective (PIP) 11.1 (2009): 98-103. As Published http://dx.doi.org/10.1007/s00016-008-0412-4 Publisher Birkhäuser Basel Version Original manuscript Citable link http://hdl.handle.net/1721.1/51720 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Hans Bethe, My Teachera Roman Jackiwb I sketch my experiences with Hans Bethe (1906-2005) as a teacher at Cornell University, beginning with my doctoral studies in 1961 and continuing with my work with him on an intermediate textbook on quantum mechanics. Key Words: Hans A. Bethe; Cornell University; physics teaching; nuclear physics; quantum mechanics. In recent times we have seen many appreciations and testimonials about Hans Bethe’s outstanding achievements: extraordinary breadth of physics research, significant involvement with social, political, and policy issues, important activity in the industrial and technological arenas. I am sure Hans would be pleased with these encomiums. But perhaps he would wonder why there is little mention of his qualities as pedagogue. After all, Professor Bethe was fundamentally a teacher, imparting his knowledge not only to physics colleagues, not only to people in society, government, and industry, but most importantly also to students, many of whom became distinguished physicists. Even though he received the Oersted Medal of the American Association of Physics Teachers in 1983 for his teaching, I think that this aspect of his a Based on my talk at the Bethe Memorial, Aspen Center for Physics, Aspen, CO, in August 2006.
    [Show full text]
  • Quantum [Un]Speakables Springer-Verlag Berlin Heidelberg Gmbh
    Quantum [Un]speakables Springer-Verlag Berlin Heidelberg GmbH ONLINE LIBRARY Physics and Astronomy http://www.springer.de/phys/ R.A. Bertlmann A. Zeilinger Quantum [Un]speakables From Bell to Quantum Information With 141 Figures, 4 in Color t Springer Professor Dr. Reinhold A. Bertlmann University of Vienna, Institute for Theoretical Physics Boltzmanngasse 5, 1090 Vienna, Austria e-mail: [email protected] Professor Dr. Anton Zeilinger University of Vienna, Institute for Experimental Physics Boltzmanngasse 5, 1090 Vienna, Austria e-mail: [email protected] Library of Congress Cataloging-in-Publication Data Quantum [un]speakables : from Bell to quantum information I [edited by] R.A. Bertimann, A. Zeilinger. p. cm. Includes biblographical references and index. ISBN 3540427562 (acid-free pa­ per) 1. Bell's theorem--Congresses. 3. Bell, J.S.--Congress. I. Bell, J.S. II. Bertlmann, Reinhold A. III. Zeilinger, Anton. QC174.17.B45 Q36 2002 530.12--dc21 2002021641 ISBN 978-3-642-07664-0 ISBN 978-3-662-05032-3 (eBook) DOI 10.1007/978-3-662-05032-2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law.
    [Show full text]
  • Two Quantum Effects in the Theory of Gravitation
    Two Quantum Effects in the Theory of Gravitation by Sean Patrick Robinson S.B., Physics, Massachusetts Institute of Technology (1999) Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2005 © Sean Patrick Robinson, MMV. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part. MASSCHUSETSSE OF TECHNOLOGY JUN 0 7 2005 Au th or ............................. ....-............. ...............LIBRARIES Department of Physics May 19, 2005 Certified by -/ 'I C ertifi ed by......... .............. -... ............................. Frank Wilczek Herman Feshbach Professor of Physics Thesis Supervisor ~~~~~ ~~~~/ A ccepted by ........................... Professr Thom/Greytak Associate Department Head fo ducation Two Quantum Effects in the Theory of Gravitation by Sean Patrick Robinson Submitted to the Department of Physics on May 19, 2005, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics Abstract We will discuss two methods by which the formalism of quantum field theory can be included in calculating the physical effects of gravitation. In the first of these, the consequences of treating general relativity as an effective quantum field theory will be examined. The primary result will be the calculation of the first-order quantum gravity corrections to the /3 functions of arbitrary Yang-Mills theories. These correc- tions will effect the high-energy phenomenology of such theories, including the details of coupling constant unification. Following this, we will address the question of how to form effective quantum field theories in classical gravitational backgrounds.
    [Show full text]