DOCSLIB.ORG

Supersymmetry 1970-1976

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Supersymmetry 1970-1976 Too Beautiful to Ignore Supersymmetry 1970-1976 Pierre Ramond University of Florida Dirac’s 1939 James Scott Prize Lecture on the relation between Mathematics and Physics Experiment and Observation Mathematical Reasoning Newton: Simplicity Einstein: Mathematical Beauty where simplicity and beauty clash … Opt for Beauty! some concepts are too beautiful to ignore: Supersymmetry 1970-1976 1939: Wigner finds two weird massless “Infinite Spin” representations with different helicity strings 5 3 1 1 3 5 , , , , + , + , + , ··· −2 −2 −2 2 2 2 ··· ? , 2, 1, 0, +1, +2, ··· − − ··· Supersymmetry born on both sides of the iron curtain in 1970 5 from S-Matrix to Superstrings PREDICTION OF REGC}E PARAMETERSIOF p POLES FROM L.oW-ENERGY rN DATA* R. Dolen, D. Hornrf and C. Schmid Callfornta Inatltute of Technologr, Paaadens, Callfornla (Received 23 June 1967) Uslng flnlte-etrerry sum rulea we predlct lmportint features of the Regge structuxe of p polee from low-enerry rN data. The comblned effect of N* resonanrces in generatlng (via the sum rules) propertles of the anolunged p polee ls disoussed, thus startlng a neur type of bootetrap caloulation. 6 π - N scattering resonances Imyfr, Regge pole boson-fermion! 7 Veneziano Model (bosons only) = extract vertex & propagator from amplitudes 8 String Model 1 2 2 L0 = p + oscillators = P P L0 + m · Pµ = pµ + (oscillators)µ ik Q ˙ e · Pµ = Qµ 9 µ Dirac equation γµ p + m =0 Pµ = pµ + (oscillators)µ 10 Generalized Dirac equation ΓµPµ + m =0 Γ , Γ = ⌘ { µ ⌫ } µ⌫ γ Γ = γ + γ (oscillators) µ ! µ µ 5 µ “The α’s are new dynamical variables which it is necessary to introduce in order to satisfy the conditions of the problem. They may be regarded as describing some internal motion of the electron. …. We shall call them the spin variables.” (Dirac) 11 Dirac structure requires anticommuting oscillators with vector indices learned much later that in D=10 space-time dimensions, the little group vector and spinor have the same dimension Mercedes Dynkin diagram! . 12 new kind of symmetry (square root of the Virasoro algebra) F ,F =2L [ L ,F ]=(2m n)F { n m } n+m n m − m+n [ L ,L ]=(m n)L n m − m+n Ln generate the (2-d conformal) Virasoro algebra Fn generate 2-d superconformal algebra 2-d supersymmetry 13 Superstring amplitudes Dual Pion Model = fermion boson 14 Dual Pion Model fermion and boson: same theory different boundary conditions 15 long soviet winters, long soviet summers, also lead to supersymmetry 16 Berezin & Kac, 1970 17 Gol’fand & Likhtman, 1971 extension of space-time symmetry 18 posit super-invariant interaction between Wess-Zumino and gauge multiplets (not quite right) nobody notices 19 Volkov & Akulov, 1972 neutrino as a Nambu-Goldstone particle a 0 = + ⇣ xµ x0 (⇣†σµ †σµ⇣) ! ! µ − 2i − nonlinear super σ-model “ … if we introduce gauge fields corresponding to the(se) transformations, then as a consequence of the Higgs effect, a massive gauge field with spin 3/2 arises and the Goldstone particle with spin 1/2 vanishes” 20 1970 Russians Superstrings 1973 WZ 1976 Sugra MSSM 21 Wess & Zumino, 1973 from the superstring side to four dimensions free scalar and vector supermultiplets with auxiliary fields 22 Wess & Zumino, 1974 one loop structure of WZ multiplet no quadratic divergences Likthman, 1975 only wave function renormalization Källen, 1949 23 CPT 1 1 Super Poincaré Group (λ, λ + ) + ( λ, λ ) 2 − − − 2 Two helicities multiplets Wess-Zumino SuperGauge SuperGravity Gol’fand-Likthman self-conjugate multiplets (Gell-Mann 1974) 1 1 N=4 Super Yang-Mills 1 +4 +6 0 +4 + 1 2 − 2 − ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ N=8 SuperGravity 3 1 1 3 2 +8 + 28 1 + 56 + 70 0 + 56 + 28 1 +8 + 2 2 2 − 2 − − 2 − ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ 24 Fayet 1974 Super Higgs mechanism R-symmetry neutrino as Goldstone fermion 25 1976 Freedman, van Nieuwenhuisen & Ferrara N=1 Supergravity graviton-gravitino interacting theory 26 1976 Brink, Schwarz & Scherk interacting N=4 SuperYang-Mills 27 1976 Gliozzi, Olive & Scherk comes full circle supersymmetric string in ten dimensions 28 1976 Gildener & Weinberg gauge hierarchy 29 1976 Fayet Birth of the Supersymmetric Standard Model two scalar superfields leptons & quarks in WZ multiplets continuous R-symmetry 30 Superstrings still in flight IIA HET M IIB HET’ I 31 Plato’s Cave Coset Physics 32 1931 Blanche Calloway “It Looks like Susie” 33 It looks like Susie It must be Susie I’m sure it’s Susie But I don’t know Could be Virginia With her eyes of Blue Could be Mary Sweet MaryLou But it looks like Susy She talks like Susy She walks like Susy . 34.
Load more

Recommended publications
  • Florida Physics News University of Florida - Department of Physics Annual Alumni Newsletter 2005
    Florida Physics News University of Florida - Department of Physics Annual Alumni Newsletter 2005 University of Florida - Department of Physics 1 Contents Chair’s Corner 2 Chair’s Corner UF Teacher/Scholar Award 3 American Physical Society - Three New Fellows 5 APS Keithley Award 5 November 2005 marks the third anniversary of Professors Earn Positions in National Societies 6 my term as department chair, and I can say that the Columbia Shuttle Accident Investigation 7 Student Government Award 8 past year has been the most exciting one (“exciting” Academy Induction 8 in the sense of the ancient Chinese curse, “May you Faculty Promotions 8 Post-Doc Awarded Fellowship from L’Oreal Corporation 8 live in exciting times”). Two significant events come to Research Scholar Award 8 mind: the record 2004 hurricane season, and the July Travel Awards 9 Undergraduate Physics Newsletter - In Review 10 2004 implementation of the new Enterprise Resource Albert Einstein Institut Rewards Two Students 12 Planning so�ware from PeopleSo�, designed to Physics Teacher of the Year 12 manage UF’s financial, payroll, and human resources 25th Brandt-Ritchie Workshop 12 TannerFest 12 activities. As you know, Florida was hammered 45th Sanibel Symposium 13 by four hurricanes during last year’s season, and Faculty Retirement 13 Faculty Selected Publications 14 Hurricanes Frances and Jeanne directly hit Gainesville Davis Productivity Award 16 in September 2004. Although ultimately the damage to Staff Retirement 16 Employee Excellence Awardees 16 UF was minimal, with downed trees, power outages, Undergraduate Honors 16 and minor flooding, it was nonetheless a stressful time Outreach Program 17 Celebrating New PhD’s 18 for the many faculty, staff, and students who were Awards Made Possible By Alumni Donations 18 affected by the storms.
    [Show full text]
  • Fermilab Theory Group
    Fermilab Theory Group Christopher T. Hill DOE Annual Program Review Fermilab, May 17, 2006 Scale of Effort(s) Program Review FY05 FY06 FY07 FY08 Particle Theory (SWF+M&S+G&V) $3,598 $3,531 $3,731 $3,899 Lattice $1,451 $2,782 $2,733 $3,035 The support for the Lattice gauge is increasing; some of the funds come from SciDAC, some from the core budget. Scientists (12) Associate Scientists (1) Research Associates (9) Bill Bardeen Thomas Becher (9/04) Mu-Chun Chen Marcela Carena Richard Hill Estia Eichten Jay Hubicz Keith Ellis Jim Laiho Walter Giele Olga Mena Christopher Hill Senior Guest Scientist(1) Enrico Lunghi Andreas Kronfeld Jose Santiago Boris Kayser Joe Lykken Peter Skands Paul Mackenzie Ruth van de Water Bogdan Dobrescu* Emeritus Scientist (1) Regular Users Stephen Parke Leon M. Lederman C. Albright (NIU) Chris Quigg S. Mrenna (Fermilab, Computing) Y. Keung (UIC) *Promoted, 10/01/05 S.P. Martin (NIU) Ulrich Baur (Buffalo) Departures: Associate Scientist Search: Ayres Freitas Zurich ETH Babis Anastasiou (offered and declined) Giulia Zanderighi CERN Uli Haisch Zurich ETH History of the Post-Docs, Associate Masataka Okamoto KEK Scientists and Frontier Fellows is Ulrich Nierste Karlsruhe (Professor) posted on the web: http://theory.fnal.gov/people/ellis/alumni.html New Postdoc Hires arrived Fall 2005: http://theory.fnal.gov/people/ellis/Assoc.html Mu-Chun Chen (from BNL),(*) http://theory.fnal.gov/people/ellis/frontier.html Richard Hill (from SLAC), Jay Hubicz (from Cornell) Enrico Lunghi (from ETH) Ruth van de Water (from Seattle) (*) just received Jr. Faculty offer from Irvine New Postdoc Hires to arrive Fall 2006: K.
    [Show full text]
  • The Early Years of String Theory: a Personal Perspective
    CALT-68-2657 THE EARLY YEARS OF STRING THEORY: A PERSONAL PERSPECTIVE John H. Schwarz California Institute of Technology Pasadena, CA 91125, USA Abstract arXiv:0708.1917v3 [hep-th] 3 Apr 2009 This article surveys some of the highlights in the development of string theory through the first superstring revolution in 1984. The emphasis is on topics in which the author was involved, especially the observation that critical string theories provide consistent quantum theories of gravity and the proposal to use string theory to construct a unified theory of all fundamental particles and forces. Based on a lecture presented on June 20, 2007 at the Galileo Galilei Institute 1 Introduction I am happy to have this opportunity to reminisce about the origins and development of string theory from 1962 (when I entered graduate school) through the first superstring revolution in 1984. Some of the topics were discussed previously in three papers that were written for various special events in 2000 [1, 2, 3]. Also, some of this material was reviewed in the 1985 reprint volumes [4], as well as the string theory textbooks [5, 6]. In presenting my experiences and impressions of this period, it is inevitable that my own contributions are emphasized. Some of the other early contributors to string theory have presented their recollections at the Galileo Galilei Institute meeting on “The Birth of String Theory” in May 2007. Since I was unable to attend that meeting, my talk was given at the GGI one month later. Taken together, the papers in this collection should
    [Show full text]
  • STRING THEORY in the TWENTIETH CENTURY John H
    STRING THEORY IN THE TWENTIETH CENTURY John H. Schwarz Strings 2016 { August 1, 2016 ABSTRACT String theory has been described as 21st century sci- ence, which was discovered in the 20th century. Most of you are too young to have experienced what happened. Therefore, I think it makes sense to summarize some of the highlights in this opening lecture. Since I only have 25 minutes, this cannot be a com- prehensive history. Important omitted topics include 2d CFT, string field theory, topological string theory, string phenomenology, and contributions to pure mathematics. Even so, I probably have too many slides. 1 1960 { 68: The analytic S matrix The goal was to construct the S matrix that describes hadronic scattering amplitudes by assuming • Unitarity and analyticity of the S matrix • Analyticity in angular momentum and Regge Pole The- ory • The bootstrap conjecture, which developed into Dual- ity (e.g., between s-channel and t-channel resonances) 2 The dual resonance model In 1968 Veneziano found an explicit realization of duality and Regge behavior in the narrow resonance approxima- tion: Γ(−α(s))Γ(−α(t)) A(s; t) = g2 ; Γ(−α(s) − α(t)) 0 α(s) = α(0) + α s: The motivation was phenomenological. Incredibly, this turned out to be a tree amplitude in a string theory! 3 Soon thereafter Virasoro proposed, as an alternative, g2 Γ(−α(s))Γ(−α(t))Γ(−α(u)) T = 2 2 2 ; −α(t)+α(u) −α(s)+α(u) −α(s)+α(t) Γ( 2 )Γ( 2 )Γ( 2 ) which has similar virtues.
    [Show full text]
  • Superfluous Physics
    Superfluous Physics Evan Berkowitz,1, ∗ William Donnelly,2 and Sylvia Zhu3, 4 (Scientists Undertaking Preposterous Etymological Research Collaboration) 1Institut f¨ur Kernphysik and Institute for Advanced Simulation, Forschungszentrum J¨ulich, 54245 J¨ulich Germany 2Perimeter Institute for Theoretical Physics, 31 Caroline St. N. Waterloo, ON, N2L 2Y5, Canada 3Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Callinstraße 38, 30167 Hannover Germany 4Leibniz Universit¨at Hannover, D-30167 Hannover, Germany (Dated: April 1, 2019) A superweapon of modern physics superscribes a wide superset of phenomena, ranging from supernumerary rainbows to superfluidity and even possible supermultiplets. I. INTRODUCTION The questions run too deep For such a simple man Won’t you please, Please tell me what we’ve learned? Supertramp, The Logical Song Supermassive black holes have nonzero supermass, the quantity that couples to N = 1 supergravity, while in theories with more supercharges one may have superdupermassive black holes, and so on. Just as the no-hair theorem tells us that non-rotating black holes can be described as massive and charged, the no-hair supertheorem tell us that non-rotating superheavy black holes can be described as supermassive and supercharged. String theory provides hope to understand how to go beyond the semiclassical limit to describe in detail if and how black holes preserve unitarity, while superstring theory provides hope to understand the unitarity of supermassive black holes. With the recent observation of normal black hole [1–5] and neutron star[6] mergers via gravitational waves by the super-sensitive Advanced LIGO and VIRGO detectors, it is not unreasonable to expect gravitational-wave detections of supernovae of collapsing superstars or violent supermassive black hole astrophysical phenomena are on the horizon or, if you’ll forgive the absurd pun, superhorizon.
    [Show full text]
  • The Birth of String Theory
    The Birth of String Theory Edited by Andrea Cappelli INFN, Florence Elena Castellani Department of Philosophy, University of Florence Filippo Colomo INFN, Florence Paolo Di Vecchia The Niels Bohr Institute, Copenhagen and Nordita, Stockholm Contents Contributors page vii Preface xi Contents of Editors' Chapters xiv Abbreviations and acronyms xviii Photographs of contributors xxi Part I Overview 1 1 Introduction and synopsis 3 2 Rise and fall of the hadronic string Gabriele Veneziano 19 3 Gravity, unification, and the superstring John H. Schwarz 41 4 Early string theory as a challenging case study for philo- sophers Elena Castellani 71 EARLY STRING THEORY 91 Part II The prehistory: the analytic S-matrix 93 5 Introduction to Part II 95 6 Particle theory in the Sixties: from current algebra to the Veneziano amplitude Marco Ademollo 115 7 The path to the Veneziano model Hector R. Rubinstein 134 iii iv Contents 8 Two-component duality and strings Peter G.O. Freund 141 9 Note on the prehistory of string theory Murray Gell-Mann 148 Part III The Dual Resonance Model 151 10 Introduction to Part III 153 11 From the S-matrix to string theory Paolo Di Vecchia 178 12 Reminiscence on the birth of string theory Joel A. Shapiro 204 13 Personal recollections Daniele Amati 219 14 Early string theory at Fermilab and Rutgers Louis Clavelli 221 15 Dual amplitudes in higher dimensions: a personal view Claud Lovelace 227 16 Personal recollections on dual models Renato Musto 232 17 Remembering the `supergroup' collaboration Francesco Nicodemi 239 18 The `3-Reggeon vertex' Stefano Sciuto 246 Part IV The string 251 19 Introduction to Part IV 253 20 From dual models to relativistic strings Peter Goddard 270 21 The first string theory: personal recollections Leonard Susskind 301 22 The string picture of the Veneziano model Holger B.
    [Show full text]
  • E6, Strings, Branes, and the Standard Model
    CERN-CDS-EXT-2004-031 TS-04-4 April 2004 E6, Strings, Branes, and the Standard Model Frank D. (Tony) Smith, Jr. e-mail: [email protected] P. O. Box 370, Cartersville, GA 30120 USA WWW URL: http://www.innerx.net/personal/tsmith/TShome.html Abstract E6,anexceptional Lie algebra, contains generators with spinor fermionic characteristics, providing a way to include fermions in string theory without 1-1 boson-fermion supersymmetry. E6 graded structure E6 = g(−2) + g(−1) + g(0) + g(1) + g(2) can be used to construct a physically realistic representation of the 26-dimensions of string theory in which strings are interpreted as world-lines in a Many-Worlds quantum picture. This paper describes the construction step-by-step. The resulting physical interpretation is consistent with the physics model described in physics/0207095 [8] . Contents 1 String Theory, Exceptional Lie Algebra E6 and Fermions 2 1.1 26-dim Traceless Jordan J3(O)o and Exceptional Lie algebra E6 2 1.2 E6 as a 5-graded Lie algebra . .................. 4 1.3 E6 and 28 gauge bosons, 8-dim spacetime and 8 sets of fermion particles and antiparticles . .................. 5 1.4 4-dim Internal Symmetry Space and 4-dim Physical Spacetime 6 2 Strings, Branes, and the Standard Model 7 2.1 Step 1 - 26-dim J3(O)o ...................... 12 2.2 Step 2 - D3 of Quaternionic substructure of Octonionic space . 12 2.3 Step 3 - Compactify 4-dim Internal Symmetry Space and make D7 ................................. 12 2.4 Step 4 - Orbifold to discretize time and make D8 .
    [Show full text]
  • Arxiv:Hep-Th/0501079 V2 15 Jan 2005
    UFIFT-HEP-05-01 Eleven-Dimensional Supergravity in Light-Cone Superspace Sudarshan Ananth1, Institute for Fundamental Theory, Department of Physics, University of Florida Gainesville FL 32611, USA Lars Brink, Department of Theoretical Physics Chalmers University of Technology, S-412 96 G¨oteborg, Sweden Pierre Ramond 2 Institute for Fundamental Theory, Department of Physics, University of Florida Gainesville FL 32611, USA arXiv:hep-th/0501079 v2 15 Jan 2005 Abstract We show that Supergravity in eleven dimensions can be described in terms of a constrained superfield on the light-cone, without the use of auxiliary fields. We build its action to first order in the gravitational coupling constant κ, by “oxidizing” ( =8 , d = 4) Supergravity. This is simply achieved, as for =4 Yang-Mills, byN extending the transverse derivatives into superspace. The eleven-N dimensional SuperPoincar´ealgebra is constructed and a fourth order interaction is conjectured. 1Supported by a McLaughlin Fellowship from the University of Florida and in part by the US Department of Energy under grant DE-FG02-97ER41029 2Supported in part by the US Department of Energy under grant DE-FG02-97ER41029 1 Introduction = 1 supergravity in eleven dimensions [1], is the largest supersymmetric localN field theory with maximum helicity two (on reduction to d = 4). This theory has gained renewed prominence since its recognition as the infrared limit of M-Theory [2]. Although M-Theory casts well-defined shadows on lower- dimensional manifolds, its actual structure remains a mystery. We must there- fore glean all we can from the = 1 supergravity theory before tackling M- Theory. = 1 supergravity isN ultraviolet divergent in d = 11 but this diver- gence is presumablyN tamed by M-Theory and the hope is that an understanding of this divergent structure, will give us a window into the workings of M-Theory.
    [Show full text]
  • Superstring Theory -- Have Oscillation Modes That Correspond to Massless Particles
    STRING THEORY John H. Schwarz Sao Paulo September 4, 2013 1 OUTLINE I) Early History and Basic Concepts II) String Theory for Unification III) Superstrings IV) Conclusion 2 I) Early History and Basic Concepts String theory arose in the late 1960s in an attempt to understand the strong nuclear force. This is the force that holds protons and neutrons together inside the nucleus of an atom. The strong nuclear force also hold quarks and gluons together inside the neutron and proton. Strongly interacting particles, such as the proton and neutron, are called hadrons. 3 A correct theory must incorporate the well- established principles of special relativity and quantum mechanics. A theory of this type, based on point-like particles, is called a quantum field theory. In addition to the strong nuclear force, the other known fundamental forces are electromagnetism, the weak nuclear force, and gravity. 4 Strings are physical objects that are curves in space. They have energy density or tension, just as point particles have mass. A theory based on strings can account for various features of the strong nuclear force such as the rich spectrum of hadrons and the high- energy behavior of interactions. The first string theory was developed in the period 1968-70 by Gabriele Veneziano and hundreds of others. 5 Two possible topologies for strings Open strings have two ends: Closed strings are loops without any ends: 6 The Basic Idea Different modes of oscillation (or quantum states) of the string behave as different particles. So, in this sense, there is a unique object (namely, the string).
    [Show full text]
  • String Theory: the Early Years, a Personal Perspective, by John H
    STRING THEORY – THE EARLY YEARS A PERSONAL PERSPECTIVE John H. Schwarz Galileo Galilei Institute – June 20, 2007 Introduction Some of my material has appeared previously in three papers that I wrote in 2000 (hep-th/0007117, 0007118, 0011078). There is also some historical material in the reprint volumes I edited in 1985 and the textbooks I coau- thored in 1987 and 2007. The GGI May 2007 Meeting The Birth of String Theory featured talks by Ademollo, Veneziano, Di Vecchia, Fairlie, Ramond, Neveu, Gliozzi, Green. Their slides are on the GGI website. 1 OUTLINE • 1960 – 68: The analytic S matrix (Ademollo, Veneziano) • 1968 – 70: The dual resonance model (Veneziano, Di Vecchia, Fairlie, Neveu) • 1971 – 73: The NSR model (Ramond, Neveu) • 1974 – 75: Gravity and unification • 1975 – 79: Supersymmetry and supergravity (Gliozzi) • 1979 – 84: Superstrings and anomalies (Green) 2 1960 – 68: The analytic S matrix GOAL: Theory of hadrons. UC Berkeley was center of the Universe (Chew, Mandel- stam, Weinberg, Glashow, . ) I was a graduate student there 1962 – 66 (so was David Gross). Geoff Chew was my advisor. He inculcated the following principles, which prepared me well for my career as a string theorist. 3 PRINCIPLES • Only the S matrix is physical. Field theory is misguided (except for QED). • Unitarity and analyticity • Analyticity in angular momentum. This developed into Regge Pole Theory • Bootstrap conjecture This developed into Duality. 4 5 6 1968 – 70: The dual resonance model Veneziano formula: T = A(s, t) + A(s, u) + A(t, u) Γ(−α(s))Γ(−α(t)) A(s, t) = Γ(−α(s) − α(t)) where α(s) = α(0) + α0s This formula gives an explicit realization of duality and Regge behavior in the narrow resonance approximation.
    [Show full text]
  • Pierre Ramond University of Florida
    The Birth of Supersymmetry (1970-1976) Pierre Ramond University of Florida still alive 1 Supersymmetry born on both sides of the iron curtain 2 in the west S-Matrix to Superstrings PREDICTION OF REGC}E PARAMETERSIOF p POLES FROM L.oW-ENERGY rN DATA* R. Dolen, D. Hornrf and C. Schmid Callfornta Inatltute of Technologr, Paaadens, Callfornla (Received 23 June 1967) Uslng flnlte-etrerry sum rulea we predlct lmportint features of the Regge structuxe of p polee from low-enerry rN data. The comblned effect of N* resonanrces in generatlng (via the sum rules) propertles of the anolunged p polee ls disoussed, thus startlng a neur type of bootetrap caloulation. 3 π - N scattering resonances Imyfr, Regge pole 4 π - N scattering boson π π fermion N N fermion boson 5 Veneziano Model (bosons only) = extract vertex & propagator from amplitudes 6 String Model 1 2 2 L0 = p + oscillators = P P L0 + m · Pµ = pµ + (oscillators)µ ik Q ˙ e · Pµ = Qµ 7 µ Dirac equation γµ p + m =0 Pµ = pµ + (oscillators)µ 8 Generalized Dirac equation ΓµPµ + m =0 Γ , Γ = ⌘ { µ ⌫ } µ⌫ γ Γ = γ + γ (oscillators) µ ! µ µ 5 µ “The α’s are new dynamical variables which it is necessary to introduce in order to satisfy the conditions of the problem. They may be regarded as describing some internal motion of the electron. …. We shall call them the spin variables.” (Dirac) 9 Dirac structure requires anticommuting oscillators with vector indices!!!! Spin-Statistics? learned much later that in D=10 space-time dimensions, the little group vector and spinor have the same dimension Mercedes-Benz Dynkin diagram! .
    [Show full text]
  • The Sirens of Eleven Dimensions
    The Sirens of Eleven Dimensions Pierre Ramond1 Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA While most theorists are tied to the mast of four dimensions, some have found it irresistible to speculate about eleven dimensions, the domain of M-theory. We outline a program which starts from the light-cone description of supergravity, and tracks its divergences to suggest the existence of an infinite component theory which in the light-cone relies on the coset F4/SO(9), long known to be linked to the Exceptional Jordan Algebra 1 Souvenirs I met Ian Kogan more than ten years ago. I remember him as being interested in everything, attacking problems like a cavalry captain, fearlessly and enthusiasti- cally. Growing up in the Soviet Union, he was neither a particle nor a condensed matter physicist, he was simply put, a physicist. I recall his gracious invitation to lunch in Oxford a few days after the birth of his child! Ian impressed all around him with his child-like interest in new ideas, uninhibited imagination, incredible energy and obvious love of physics. His premature loss is one of those events in life that leave everyone who knew him, sadly diminished. arXiv:hep-th/0411024v1 1 Nov 2004 To honor Ian’s memory, I wanted to write something substantive and spec- ulative enough to have aroused his interest. Thus follows a description of a program that has occupied me for the last seven years. It has not yet reached the stage of obvious physical import, but it has unearthed unique mathematical structures, and raised the specter of a singular theory in eleven dimensions with an infinite number of massless particles of arbitrarily high helicities.
    [Show full text]