DOCSLIB.ORG

Wolfhart Zimmermann: Life and Work

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Wolfhart Zimmermann: Life and Work JID:NUPHB AID:14268 /FLA [m1+; v1.280; Prn:28/02/2018; 9:46] P.1(1-11) Available online at www.sciencedirect.com ScienceDirect Nuclear Physics B ••• (••••) •••–••• www.elsevier.com/locate/nuclphysb Wolfhart Zimmermann: Life and work Klaus Sibold Institut für Theoretische Physik, Universiät Leipzig, Postfach 100920, D-04009 Leipzig, Germany Received 19 December 2017; received in revised form 17 January 2018; accepted 22 January 2018 Editor: Hubert Saleur Abstract In this report, I briefly describe the life and work of Wolfhart Zimmermann. The highlights of his scien- tific achievements are sketched and some considerations are devoted to the man behind the scientist. The report is understood as being very personal: at various instances I shall illustrate facets of work and person by anecdotes. © 2018 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction The present report is based on a colloquium talk given at the end of a memorial symposium to honour Wolfhart Zimmermann: Max Planck Institute for Physics, Munich (May 22–23, 2017) I borrowed freely from the following obituaries: Physik-Journal 15 (2016) Nr. 12 S.50 W. Hollik, E. Seiler, K. Sibold Nucl. Phys. B193 (2016) 877–878 W. Hollik, E. Seiler, K. Sibold IAMP News Bulletin, Jan. 2017 p. 26–30 M. Salmhofer, E. Seiler, K. Sibold 2. The beginning Wolfhart Zimmermann was born on February 17, 1928 in Freiburg im Breisgau (Germany) as the son of a medical doctor. He had an older sister with whom he liked to play theater and, when E-mail address: [email protected]. https://doi.org/10.1016/j.nuclphysb.2018.01.022 0550-3213/© 2018 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. JID:NUPHB AID:14268 /FLA [m1+; v1.280; Prn:28/02/2018; 9:46] P.2(1-11) 2 K. Sibold / Nuclear Physics B ••• (••••) •••–••• visiting Gymnasium, to talk to in “Giganisch” – a language which he invented, because he found Latin too easy. In 1946 he entered the university in Freiburg to study mathematics and physics. As far as lectures and seminars are concerned WZ was somewhat sceptical about their useful- ness for him: “Either they were too fast or too slow for me. Either I had to think about the new content – then I was too slow. Or I understood it instantly, then I was too fast and the lecture boring.” A good measure to evaluate this statement and to put it in the right perspective is to look at the facts. Already in 1950 he finished with a doctoral degree in mathematics. His thesis was devoted to topology [1], published in [2]. He once told that he had written an earlier dissertation, but abandoned it because he found out that the main result could be proven in a much simpler way, hence considered this work as inadequate for a doctoral degree. He published a further article on topology [3]. These papers were written in style and spirit of BOURBAKI, on which he commented privately “I can read BOURBAKI like the newspaper.” 3. LSZ – the first highlight In 1952 Wolfhart Zimmermann joined the group of Werner Heisenberg at the Max-Planck- Institut für Physik in Göttingen as a Research Associate, a position which he held until 1957. Remarkably, his first physics paper [4] did not deal with quantum field theory (QFT), but with the thermodynamics of a Fermi gas in interaction. He bought his ticket to Heisenberg’s group, later called “der Feldverein”, with a paper on the bound state problem in field theory [5]. It was co-authored by Vladimir Glaser, a Croatian physicist, who was to accompany Wolfhart Zim- mermann on his scientific way for a long time. Truly famous, however, were three papers [6–8] written together with Harry Lehmann and Kurt Symanzik. They contained what later was coined the “LSZ formalism” of quantum field theory. Based on the principles of Lorentz covariance, unitarity and causality of Green functions and the S-matrix they provided the first axiomatic for- mulation of quantum field theory. Lehmann, Glaser and Zimmermann [9] then, conversely, gave sufficient conditions which a set of functions has to fulfil such that these functions give rise to a field theory in the sense of LSZ. LSZ did not refer to perturbative expansions, but nevertheless proved to be greatly successful in its perturbative realization and thus extremely powerful in practice. Until the present day it serves as the most efficient description of scattering amplitudes in particle physics. The key idea is the following: in the remote past and future a scattering experiment (idealized) deals with free particles, whereas interaction takes place only in a finite region of spacetime. The respective fields are related by the asymptotic condition: √ φ(x) −→ zφ out (x), (1) x0→±∞ in where z is a number and φ out are free fields which satisfy the field equations in 2 2 + m φ out (x) = 0, (2) in whereas φ(x) is an interacting field. The limit is understood in the weak sense, i.e. it is valid only for matrix elements. (In parentheses we note that this notion of weak convergence which is of utmost importance has presumably been introduced by LSZ for the first time in the theory of particle physics.) JID:NUPHB AID:14268 /FLA [m1+; v1.280; Prn:28/02/2018; 9:46] P.3(1-11) K. Sibold / Nuclear Physics B ••• (••••) •••–••• 3 In a scattering experiment ni particles are prepared in an initial state and go over into nf particles in the final state. The transition is described by the S-operator with matrix elements Sfi. Those are given by the famous LSZ-reduction formula = | ≡ | Sfi f i p1 ...pnf q1 ...qni (3) + nf n −1 nf ni i = √ lim (p2 − m2) (q2 − m2)G(˜ −p , ..., −p ,q , ..., q ) (4) z k j 1 nf 1 ni k=1 j=1 n nf +ni ni f i − = √ dx e iqkxk (2 + m2) dx eipj yj (2 + m2) × z k xk j yj k=1 j=1 | G(y1 ...ynf ,x1 ...xni ) 0= qk ωk 0= pj ωj 2 → 2 2 → 2 0 0 (with lim: pk m , qj m , pk > 0, qk > 0). Here G(y1, ..., ynf , x1, ..., xni ) denote the Green functions = G(y1,...,ynf ,x1,...,xni ) Tϕ(y1)...ϕ(xni ) , (5) the vacuum expectation value of the time ordered product of field operators. They thus permit to calculate the S-matrix and are themselves determined by equations of motion. An important generalization of this reduction formula expresses the matrix elements of a (composite) operator O in terms of the Green functions with an insertion (details see below). + −1 n l n l p , ..., p |O(x)|q , ..., q = √ lim (p2 − m2) (q2 − m2) × 1 n 1 l z k j k=1 j=1 ˜ × GO(x)(−p1, ..., −pn,q1, ..., ql) GO(x)(y1, ..., yn,x1, ...xl) =T O(x)ϕ(y1)...ϕ(xl) (0) (0) (0) (0) i L T O(x)ϕ(y1)...ϕ(xl)=RT : O (x) : ϕ (y1)...ϕ (xl)e h¯ int Historical remark: Another axiomatic formulation of QFT was initiated by Wightman (1956). The relation of the LSZ-scattering theory to those axioms and clarification of the role of funda- mental fields were given by Haag (1958, 1959) and in particular by Ruelle (1962). As mentioned above these formulae for Green functions and the S-matrix can be satisfied in a perturbative manner. In practice the most often employed technique is in terms of diagrams as introduced by Feynman. With every elementary interaction one associates a vertex (symbolizing the specific interaction) and emanating lines which stand for particles propagating in spacetime. x1 x2 x4 x3 A scattering process is described by diagrams where these elementary vertices are linked by lines. The vertices and lines are interpreted in terms of mathematical prescriptions, the “Feynman JID:NUPHB AID:14268 /FLA [m1+; v1.280; Prn:28/02/2018; 9:46] P.4(1-11) 4 K. Sibold / Nuclear Physics B ••• (••••) •••–••• rules”, which eventually permit to calculate Green functions and the S-matrix. In the most naive version diagrams are ordered according to the number of vertices they are made of; this results into a power series of coupling constants: the perturbation series. Since the diagrams mimic physical processes, they are intuitively appealing and, therefore were overwhelmingly used in particle physics (and beyond: e.g. in condensed matter physics). But, of course, the mathematical expressions for Feynman rules have to be derived by a consistent algorithm. Usually it exploits the Gell-mann-Low formula for Green functions G(x1, ..., xn) =T(φ(x1)...φ(xn)) (6) (0) (0) i L(0) T φ (x1)...φ (xn)e int = (7) i L(0) e int For the S-operator this is tantamount to the Dyson formula L S = Tei int (8) On this level it is (almost) evident that the fundamental axioms – Lorentz covariance, unitar- ity and causality – are satisfied. For the subsequent discussion it is crucial to observe that the propagator for a (real, spinless) field i ˜ (p) = (9) c p2 − m2 + iε is, mathematically speaking, not a function, but rather a distribution. This can be seen by cal- culating the product at the same point c(x − y)c(x − y). The result is infinite, hence apriori meaningless. It implies that many of the Feynman diagrams containing closed loops are mean- ingless. Therefore one faces the problem to give mathematical meaning to such expressions and at the same time not to violate the fundamental axioms in doing so.
Load more

Recommended publications
  • The $\Phi^ 3 4 $ and $\Phi^ 3 6 $ Matricial QFT Models Have
    Φ3 Φ3 The 4 and 6 matricial QFT models have reflection positive two-point function Harald Grosse1, Akifumi Sako1,2 and Raimar Wulkenhaar3 1 Fakult¨at f¨ur Physik, Universit¨at Wien Boltzmanngasse 5, A-1090 Wien, Austria 2 Department of Mathematics, Faculty of Science Division II, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan 3 Mathematisches Institut der Westf¨alischen Wilhelms-Universit¨at Einsteinstraße 62, D-48149 M¨unster, Germany MSC 2010: 81T16, 81T08, 81R12 dedicated to the memory of Wolfhart Zimmermann (1928–2016) Abstract We extend our previous work (on D = 2) to give an exact solution of the Φ3 large- D N matrix model (or renormalised Kontsevich model) in D = 4 and D = 6 dimensions. Induction proofs and the difficult combinatorics are unchanged compared with D = 2, but the renormalisation – performed according to Zimmermann – is much more involved. As main result we prove that the Schwinger 2-point function resulting from 3 the ΦD-QFT model on Moyal space satisfies, for real coupling constant, reflection positivity in D = 4 and D = 6 dimensions. The K¨all´en-Lehmann mass spectrum of the associated Wightman 2-point function describes a scattering part p 2 2µ2 | | ≥ and an isolated fuzzy mass shell around p 2 = µ2. | | 1 Introduction arXiv:1612.07584v2 [math-ph] 2 Jun 2017 The Kontsevich model [1, 2] is of paramount importance because it elegantly proves Witten’s conjecture [3] about the equivalence of two approaches to quantum gravity in two dimensions: the Hermitean one-matrix model [4, 5, 6] versus the intersection theory on the moduli space of Riemann surfaces [7, 8, 9].
    [Show full text]
  • Dispersion Relations in Gauge Theories with Confinement
    EFI 95-54 MPI-Ph/95-82 Dispersion Relations in Gauge Theories with Confinement 1 Reinhard Oehme Enrico Fermi Institute and Department of Physics University of Chicago, Chicago, Illinois, 60637, USA 2 and Max-Planck-Institut f¨ur Physik - Werner-Heisenberg-Institut - 80805 Munich, Germany Abstract The analytic structure of physical amplitudes is considered for gauge the- ories with confinement of excitations corresponding to the elementary fields. Confinement is defined in terms of the BRST algebra. BRST-invariant, local, composite fields are introduced, which interpolate between physical asymp- totic states. It is shown that the singularities of physical amplitudes are arXiv:hep-th/9511007v1 1 Nov 1995 the same as in an effective theory with only physical fields. In particular, there are no structure singularities (anomalous thresholds) associated with confined constituents, like quarks and gluons. The old proofs of dispersion relations for hadronic amplitudes remain valid in QCD. 1Plenary talk presented at the XVIIIth International Workshop on High Energy Physics and Field Theory, Moscow-Protvino, June 1995. To be published in the Proceedings. 2Permanent Address It is the purpose of this talk, to give a survey of the problems involved in the derivation of analytic properties of physical amplitudes in gauge theories with confinement. This report is restricted to a brief resum´eof the essential points discussed in the talk. 3 Dispersion relations for amplitudes describing reactions between hadrons, and for form factors describing the structure of particles, have long played an important rˆole in particle physics [3, 4, 5, 6]. Analytic properties of Green’s functions are fundamental for proving many important results in quantum field theory.
    [Show full text]
  • Zimmermann's Forest Formula, Infrared Divergences and the QCD
    Zimmermann's Forest Formula, Infrared Divergences and the QCD Beta Function Franz Herzog Nikhef Theory Group, Science Park 105, 1098 XG Amsterdam, The Netherlands Abstract We review Zimmermann's forest formula, which solves Bogoliubov's recur- sive R-operation for the subtraction of ultraviolet divergences in perturba- tive Quantum Field Theory. We further discuss a generalisation of the R- operation which subtracts besides ultraviolet also Euclidean infrared diver- gences. This generalisation, which goes under the name of the R∗-operation, can be used efficiently to compute renormalisation constants. We will discuss several results obtained by this method with focus on the QCD beta function at five loops as well as the application to hadronic Higgs boson decay rates at N4LO. This article summarizes a talk given at the Wolfhart Zimmermann Memorial Symposium. Keywords: Renormalization Group, QCD Email address: [email protected] (Franz Herzog) arXiv:1711.06121v1 [hep-ph] 16 Nov 2017 Preprint submitted to Nuclear Physics B November 17, 2017 1. Introduction Despite the enormous success in describing the interactions of elementary particles the appearance of ultraviolet (UV) divergences make it difficult to establish Quantum Field Theory as a fundamental theory of nature. A solution which at least grants the interpretation of Quantum Field Theories as low energy effective theories is given by the procedure of renormalisation. This is the procedure to absorb the troublesome infinities, present at small distances, into the physical parameters of the theory. An important development in the establishment of renormalisation the- ory has been the Bogoliubov-Parasiuk-Hepp-Zimmermann (BPHZ) renor- malisation scheme. This scheme was originally developed by Bogoliubov and Parasiuk [1] in terms of a recursive subtraction operation, often called Bo- goliubov's R-operation.
    [Show full text]
  • Aspects of the Many-Body Problem in Nuclear Physics
    Aspects of the Many-Body Problem in Nuclear Physics DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Alexander Signatur Dyhdalo, MSc, BSc Graduate Program in Physics The Ohio State University 2018 Dissertation Committee: Prof. Richard Furnstahl, Advisor Prof. Robert Perry Prof. Michael Lisa Prof. Junko Shigemitsu c Copyright by Alexander Signatur Dyhdalo 2018 Abstract Low-energy nuclear physics has seen a renaissance of activity recently with the advent of the nuclear effective field theory (EFT) approach, the power of renormalization group techniques, and advances in the computational cost-effectiveness and sophistication of quan- tum many-body methods. Nevertheless challenges remain in part from ambiguities of the nuclear Hamiltonian via regulator artifacts and the scaling of the many-body methods to heavier systems. Regulator artifacts arise due to a renormalization inconsistency in the nuclear EFT as currently formulated in Weinberg power counting, though their ultimate impact on nuclear observables is unknown at present. This results in a residual cutoff dependence in the EFT to all orders. We undertake an examination of these regulator artifacts using perturba- tive energy calculations of uniform matter as a testbed. Our methodology has found that the choice of regulator determines the shape of the energy phase space and that different regulators weight distinct phase space regions differently. Concerning many-body calculations, at present only phenomenological energy density functionals are able to solve for the full table of nuclides. However these functionals are currently unconnected to QCD and have no existing method for systematic improvement.
    [Show full text]
  • A Brief History of String Theory
    THE FRONTIERS COLLECTION Dean Rickles A BRIEF HISTORY OF STRING THEORY From Dual Models to M-Theory 123 THE FRONTIERS COLLECTION Series editors Avshalom C. Elitzur Unit of Interdisciplinary Studies, Bar-Ilan University, 52900, Gières, France e-mail: [email protected] Laura Mersini-Houghton Department of Physics, University of North Carolina, Chapel Hill, NC 27599-3255 USA e-mail: [email protected] Maximilian Schlosshauer Department of Physics, University of Portland 5000 North Willamette Boulevard Portland, OR 97203, USA e-mail: [email protected] Mark P. Silverman Department of Physics, Trinity College, Hartford, CT 06106, USA e-mail: [email protected] Jack A. Tuszynski Department of Physics, University of Alberta, Edmonton, AB T6G 1Z2, Canada e-mail: [email protected] Rüdiger Vaas Center for Philosophy and Foundations of Science, University of Giessen, 35394, Giessen, Germany e-mail: [email protected] H. Dieter Zeh Gaiberger Straße 38, 69151, Waldhilsbach, Germany e-mail: [email protected] For further volumes: http://www.springer.com/series/5342 THE FRONTIERS COLLECTION Series editors A. C. Elitzur L. Mersini-Houghton M. Schlosshauer M. P. Silverman J. A. Tuszynski R. Vaas H. D. Zeh The books in this collection are devoted to challenging and open problems at the forefront of modern science, including related philosophical debates. In contrast to typical research monographs, however, they strive to present their topics in a manner accessible also to scientifically literate non-specialists wishing to gain insight into the deeper implications and fascinating questions involved. Taken as a whole, the series reflects the need for a fundamental and interdisciplinary approach to modern science.
    [Show full text]
  • The Operator Product Expansion
    The Operator Product Expansion Nolan Smyth 6/10/2020 QFT 3 - Final Presentation Outline 1. The Big Picture 2. Renormalization Group Refresher/Setup 3. Introducing the Operator Product Expansion 4. Callen-Symanzik Equation for Wilson Coefficients 5. An example: QCD corrections to weak decays 1 The Big Picture The Big Picture We've spent much of this quarter learning to deal with divergences, typically those of an ultraviolet nature. These divergences led to shifting in mass parameters and coupling constants through the process of renormalization, but were otherwise rather innocuous. Renormalization gave us a great deal of freedom in that we were free to define our theory at any arbitrary momentum scale. But in order to describe the the correct physical theory, the renormalized Green's functions must be identical to the bare Green functions, up to the field strength renormalization. (n) −n=2 (n) GR (µ; x1; :::; xn) = Z Gb (x1; :::; xn) 2 The Big Picture We then asked, how would our Green's functions change if we looked at a different renormalization scale? This led to the Callen-Symanzik (renormalization group) equations. Solving these, we calculated how coupling constants and fields evolve with momentum scale. Until now, we've utilized correlation functions to perform this analysis. But we will see that it is particularly useful to study the renormalization flow at the level of the operators themselves. But to do so, we will need to deal with the non-locality of operator products. This is where we will meet the Operator Product Expansion (OPE). 3 The Big Picture After motivating the OPE, we will see that all of the interesting behavior at high energy (short distances) depends only on Wilson coefficents.
    [Show full text]
  • Applications of the Reduction of Couplings
    Applications of the Reduction of Couplings∗ Dedicated to Professor Wolfhart Zimmermann on the occasion of his 70th birthday Jisuke Kubo Institute for Theoretical Physics, Kanazawa University Kanazawa 920-1192, Japan Abstract Applications of the principle of reduction of couplings to the standard model and supersym- metric grand unified theories are reviewed. Phenomenological applications of renormalization arXiv:hep-ph/9903482v1 25 Mar 1999 group invariant sum rules for soft supersymmetry-breaking parameters are also reviewed. ∗ To appear in the Proceedings of the Ringberg Symposium on Quantum Field Theory, Tegernsee, Germany, June 1998. 1 Application to the Standard Model High energy physicists have been using renormalizability as the predictive tool, and also to decide whether or not a quantity is calculable. As we have learned in the previous talk by Professor Oehme, it is possible, using the method of reduction of couplings [1, 2, 3], to renormalize a theory with fewer number of counter terms then usually counted, implying that the traditional notion of renormalizability should be generalized in a certain sense 1. Consequently, the notion of the predictability and the calculability [5] may also be generalized with the help of reduction of couplings. Of course, whether the generalizations of these notions have anything to do with nature is another question. The question can be answered if one applies the idea of reduction of couplings to realistic models, make predictions that are specific for reduction of couplings, and then wait till experimentalists find positive results 2. In 1984 Professor Zimmermann, Klaus Sibold and myself [8] began to apply the idea of reduction of couplings to the SU(3) SU(2) U(1) gauge model for the strong and C × L × Y electroweak interactions.
    [Show full text]
  • 2Nd Semester Course Intermediate Quantum Field Theory (A Next-To-Basic Course for Primary Education)
    2nd Semester Course Intermediate Quantum Field Theory (A Next-to-Basic Course for Primary Education) Roberto Soldati October 22, 2015 Contents 1 Generating Functionals 4 1.1 The Scalar Generating Functional . 4 1.1.1 The Symanzik Functional Equation . 5 1.1.2 The Functional Integrals for Bosons . 7 1.1.3 The ζ−Function Regularization . 10 1.2 The Spinor Generating Functional . 15 1.2.1 Symanzik Equations for Fermions . 16 1.2.2 The Integration over Graßmann Variables . 20 1.2.3 The Functional Integral for Fermions . 23 1.3 The Vector Generating Functional . 27 2 The Feynman Rules 31 2.1 Connected Green's Functions . 31 2.2 Self-Interacting Neutral Scalar Field . 41 2.3 Yukawa Theory ....................... 45 2.3.1 Yukawa Determinant . 47 2.4 Quantum ElectroDynamics (QED) . 54 2.5 The Construction of Gauge Theories . 59 2.5.1 Covariant Derivative and Related Properties . 59 2.5.2 Classical Dynamics of Non-Abelian Fields . 64 2.6 Euclidean Field Theories . 68 2.7 Problems ............................ 71 3 Scattering Operator 77 3.1 The S-Matrix in Quantum Mechanics . 77 3.2 S-Matrix in Quantum Field Theory . 79 1 3.2.1 Fields in the Interaction Picture . 80 3.2.2 S-Matrix in Perturbation Theory . 81 3.2.3 LSZ Reduction Formulas . 85 3.2.4 Feynman Rules for External Legs . 92 3.2.5 Yukawa Potential ................... 98 3.2.6 Coulomb Potential . 103 3.3 Cross Section .........................108 3.3.1 Scattering Amplitude . 108 3.3.2 Luminosity .......................112 3.3.3 Quasi-Elastic Scattering .
    [Show full text]
  • GREGOR WENTZEL February 17, 1898 - August 12, 1978
    GREGOR WENTZEL February 17, 1898 - August 12, 1978 arXiv:0809.2102v1 [physics.hist-ph] 11 Sep 2008 BY PETER G.O. FREUND, CHARLES J. GOEBEL, YOICHIRO NAMBU AND REINHARD OEHME 1 Biographical sketch The initial of Gregor Wentzel's last name has found a solid place in the language of theoretical physics as the W of the fundamental WKB approxi- mation, which describes the semi-classical limit of any quantum system. Be- yond this fundamental contribution to quantum theory [1], Gregor Wentzel has played an important role in the theoretical physics of the first half of the twentieth century. Born in D¨usseldorfon 17 February, 1898, Gregor benefited from a rich and multi-faceted education. As the greatest events of his youth, Wentzel used to recall the local premi`eresof the symphonies of Gustav Mahler. A lifelong love for music was instilled in the young Gregor. During World War I he served in the army from 1917 to 1918. At the conclusion of that cataclysmic event, he continued his studies, migrating from university to university, as was customary in those days. First, until 1919 we find him at the University of Freiburg, then at the University of Greifswald, and as of 1920, just like Wolfgang Pauli and Werner Heisenberg and then later Hans Bethe among others, studying with the legendary teacher Arnold Sommerfeld at the Ludwig Maximilians University in Munich, where he obtained his Ph.D. with a thesis on Roentgen spectra [2]. Still in Munich he completed his Habilitation in 1922 and became a Privatdozent (roughly the equivalent of what today would be an assistant professor).
    [Show full text]
  • Dean Rickles a BRIEF HISTORY of STRING THEORY
    THE FRONTIERS COLLECTION Dean Rickles A BRIEF HISTORY OF STRING THEORY From Dual Models to M-Theory 123 THE FRONTIERS COLLECTION Series editors Avshalom C. Elitzur Unit of Interdisciplinary Studies, Bar-Ilan University, 52900, Gières, France e-mail: [email protected] Laura Mersini-Houghton Department of Physics, University of North Carolina, Chapel Hill, NC 27599-3255 USA e-mail: [email protected] Maximilian Schlosshauer Department of Physics, University of Portland 5000 North Willamette Boulevard Portland, OR 97203, USA e-mail: [email protected] Mark P. Silverman Department of Physics, Trinity College, Hartford, CT 06106, USA e-mail: [email protected] Jack A. Tuszynski Department of Physics, University of Alberta, Edmonton, AB T6G 1Z2, Canada e-mail: [email protected] Rüdiger Vaas Center for Philosophy and Foundations of Science, University of Giessen, 35394, Giessen, Germany e-mail: [email protected] H. Dieter Zeh Gaiberger Straße 38, 69151, Waldhilsbach, Germany e-mail: [email protected] For further volumes: http://www.springer.com/series/5342 THE FRONTIERS COLLECTION Series editors A. C. Elitzur L. Mersini-Houghton M. Schlosshauer M. P. Silverman J. A. Tuszynski R. Vaas H. D. Zeh The books in this collection are devoted to challenging and open problems at the forefront of modern science, including related philosophical debates. In contrast to typical research monographs, however, they strive to present their topics in a manner accessible also to scientifically literate non-specialists wishing to gain insight into the deeper implications and fascinating questions involved. Taken as a whole, the series reflects the need for a fundamental and interdisciplinary approach to modern science.
    [Show full text]
  • Drawing Theories Apart: the Dispersion of Feynman Diagrams In
    Drawing Theories Apart Drawing Theories Apart The Dispersion of Feynman Diagrams in Postwar Physics david kaiser The University of Chicago Press chicago and london David Kaiser is associate professor in the Program in Science, Technology, and Society and lecturer in the Department of Physics at the Massachusetts Institute of Technology. The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London C 2005 by The University of Chicago All rights reserved. Published 2005 Printed in the United States of America 14 13 12 11 10 09 08 07 06 05 1 2 3 4 5 isbn: 0-226-42266-6 (cloth) isbn: 0-226-42267-4 (paper) Library of Congress Cataloging-in-Publication Data Kaiser, David. Drawing theories apart : the dispersion of Feynman diagrams in postwar physics / David Kaiser. p. cm. Includes bibliographical references and index. isbn 0-226-42266-6 (alk. paper)—isbn 0-226-42267-4 (pbk. : alk. paper) 1. Feynman diagrams. 2. Physics—United States—History— 20th century. 3. Physics—History—20th century. I. Title. QC794.6.F4K35 2005 530.0973 0904—dc22 2004023335 ∞ The paper used in this publication meets the minimum requirements of the American National Standard for Information Sciences—Permanence of Paper for Printed Library Materials, ansi z39.48-1992. He teaches his theory, not as a body of fact, but as a set of tools, to be used, and which he has actually used in his work. John Clarke Slater describing Percy Bridgman after Bridgman won the Nobel Prize in Physics, 11 January 1947 Contents Preface and Acknowledgments xi Abbreviations xvii Chapter 1 .
    [Show full text]
  • Review Superalgebra and Fermion-Boson Symmetry
    158 Proc. Jpn. Acad., Ser. B 86 (2010) [Vol. 86, Review Superalgebra and fermion-boson symmetry By Hironari MIYAZAWAÃ1,y (Communicated by Toshimitsu YAMAZAKI, M.J.A.) Abstract: Fermions and bosons are quite dierent kinds of particles, but it is possible to unify them in a supermultiplet, by introducing a new mathematical scheme called superalgebra. In this article we discuss the development of the concept of symmetry, starting from the rotational symmetry and nally arriving at this fermion-boson (FB) symmetry. Keywords: supermultiplet, Lie algebra, hadron spectroscopy with dierent spins are grouped as symmetry mem- Introduction bers of a supermultiplet. Feza Gursey€ and Luigi Symmetry is invariance under transformation. Radicati and Bunji Sakita extended the idea to in- Right-left symmetry, the invariance under the space clude the strange particles. Here all important mesons reection, is one of the most elementary examples. are grouped in one supermultiplet, and baryons are Spherical symmetry is the invariance under the space in another. rotation. Our three dimensional space is supposed to The next question is: is it possible to incorporate be invariant under the space rotation. mesons and baryons in one symmetry multiplet? The above examples are transformations of Mesons obey Bose statistics and baryons obey Fermi space coordinates. There are other symmetries con- statistics, so they cannot be regarded as the same nected with transformations of the matter of our particles. Nevertheless, by extending the notion of world. Proton and neutron are almost identical ex- symmetry, even bosons and fermions can be grouped cept for the charge. They can be regarded as the together.
    [Show full text]