When Fields Collide
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Supergravity and Its Legacy Prelude and the Play
Supergravity and its Legacy Prelude and the Play Sergio FERRARA (CERN – LNF INFN) Celebrating Supegravity at 40 CERN, June 24 2016 S. Ferrara - CERN, 2016 1 Supergravity as carved on the Iconic Wall at the «Simons Center for Geometry and Physics», Stony Brook S. Ferrara - CERN, 2016 2 Prelude S. Ferrara - CERN, 2016 3 In the early 1970s I was a staff member at the Frascati National Laboratories of CNEN (then the National Nuclear Energy Agency), and with my colleagues Aurelio Grillo and Giorgio Parisi we were investigating, under the leadership of Raoul Gatto (later Professor at the University of Geneva) the consequences of the application of “Conformal Invariance” to Quantum Field Theory (QFT), stimulated by the ongoing Experiments at SLAC where an unexpected Bjorken Scaling was observed in inclusive electron- proton Cross sections, which was suggesting a larger space-time symmetry in processes dominated by short distance physics. In parallel with Alexander Polyakov, at the time in the Soviet Union, we formulated in those days Conformal invariant Operator Product Expansions (OPE) and proposed the “Conformal Bootstrap” as a non-perturbative approach to QFT. S. Ferrara - CERN, 2016 4 Conformal Invariance, OPEs and Conformal Bootstrap has become again a fashionable subject in recent times, because of the introduction of efficient new methods to solve the “Bootstrap Equations” (Riccardo Rattazzi, Slava Rychkov, Erik Tonni, Alessandro Vichi), and mostly because of their role in the AdS/CFT correspondence. The latter, pioneered by Juan Maldacena, Edward Witten, Steve Gubser, Igor Klebanov and Polyakov, can be regarded, to some extent, as one of the great legacies of higher dimensional Supergravity. -
Twenty Years of the Weyl Anomaly
CTP-TAMU-06/93 Twenty Years of the Weyl Anomaly † M. J. Duff ‡ Center for Theoretical Physics Physics Department Texas A & M University College Station, Texas 77843 ABSTRACT In 1973 two Salam prot´eg´es (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor 2 gµν(x) Ω (x)gµν (x) displayed by classical massless field systems in interac- tion with→ gravity no longer survives in the quantum theory. Since then these Weyl anomalies have found a variety of applications in black hole physics, cosmology, string theory and statistical mechanics. We give a nostalgic re- view. arXiv:hep-th/9308075v1 16 Aug 1993 CTP/TAMU-06/93 July 1993 †Talk given at the Salamfest, ICTP, Trieste, March 1993. ‡ Research supported in part by NSF Grant PHY-9106593. When all else fails, you can always tell the truth. Abdus Salam 1 Trieste and Oxford Twenty years ago, Derek Capper and I had embarked on our very first post- docs here in Trieste. We were two Salam students fresh from Imperial College filled with ideas about quantizing the gravitational field: a subject which at the time was pursued only by mad dogs and Englishmen. (My thesis title: Problems in the Classical and Quantum Theories of Gravitation was greeted with hoots of derision when I announced it at the Cargese Summer School en route to Trieste. The work originated with a bet between Abdus Salam and Hermann Bondi about whether you could generate the Schwarzschild solution using Feynman diagrams. You can (and I did) but I never found out if Bondi ever paid up.) Inspired by Salam, Capper and I decided to use the recently discovered dimensional regularization1 to calculate corrections to the graviton propaga- tor from closed loops of massless particles: vectors [1] and spinors [2], the former in collaboration with Leopold Halpern. -
SHELDON LEE GLASHOW Lyman Laboratory of Physics Harvard University Cambridge, Mass., USA
TOWARDS A UNIFIED THEORY - THREADS IN A TAPESTRY Nobel Lecture, 8 December, 1979 by SHELDON LEE GLASHOW Lyman Laboratory of Physics Harvard University Cambridge, Mass., USA INTRODUCTION In 1956, when I began doing theoretical physics, the study of elementary particles was like a patchwork quilt. Electrodynamics, weak interactions, and strong interactions were clearly separate disciplines, separately taught and separately studied. There was no coherent theory that described them all. Developments such as the observation of parity violation, the successes of quantum electrodynamics, the discovery of hadron resonances and the appearance of strangeness were well-defined parts of the picture, but they could not be easily fitted together. Things have changed. Today we have what has been called a “standard theory” of elementary particle physics in which strong, weak, and electro- magnetic interactions all arise from a local symmetry principle. It is, in a sense, a complete and apparently correct theory, offering a qualitative description of all particle phenomena and precise quantitative predictions in many instances. There is no experimental data that contradicts the theory. In principle, if not yet in practice, all experimental data can be expressed in terms of a small number of “fundamental” masses and cou- pling constants. The theory we now have is an integral work of art: the patchwork quilt has become a tapestry. Tapestries are made by many artisans working together. The contribu- tions of separate workers cannot be discerned in the completed work, and the loose and false threads have been covered over. So it is in our picture of particle physics. Part of the picture is the unification of weak and electromagnetic interactions and the prediction of neutral currents, now being celebrated by the award of the Nobel Prize. -
Some Comments on Physical Mathematics
Preprint typeset in JHEP style - HYPER VERSION Some Comments on Physical Mathematics Gregory W. Moore Abstract: These are some thoughts that accompany a talk delivered at the APS Savannah meeting, April 5, 2014. I have serious doubts about whether I deserve to be awarded the 2014 Heineman Prize. Nevertheless, I thank the APS and the selection committee for their recognition of the work I have been involved in, as well as the Heineman Foundation for its continued support of Mathematical Physics. Above all, I thank my many excellent collaborators and teachers for making possible my participation in some very rewarding scientific research. 1 I have been asked to give a talk in this prize session, and so I will use the occasion to say a few words about Mathematical Physics, and its relation to the sub-discipline of Physical Mathematics. I will also comment on how some of the work mentioned in the citation illuminates this emergent field. I will begin by framing the remarks in a much broader historical and philosophical context. I hasten to add that I am neither a historian nor a philosopher of science, as will become immediately obvious to any expert, but my impression is that if we look back to the modern era of science then major figures such as Galileo, Kepler, Leibniz, and New- ton were neither physicists nor mathematicans. Rather they were Natural Philosophers. Even around the turn of the 19th century the same could still be said of Bernoulli, Euler, Lagrange, and Hamilton. But a real divide between Mathematics and Physics began to open up in the 19th century. -
Particle & Nuclear Physics Quantum Field Theory
Particle & Nuclear Physics Quantum Field Theory NOW AVAILABLE New Books & Highlights in 2019-2020 ON WORLDSCINET World Scientific Lecture Notes in Physics - Vol 83 Lectures of Sidney Coleman on Quantum Field Field Theory Theory A Path Integral Approach Foreword by David Kaiser 3rd Edition edited by Bryan Gin-ge Chen (Leiden University, Netherlands), David by Ashok Das (University of Rochester, USA & Institute of Physics, Derbes (University of Chicago, USA), David Griffiths (Reed College, Bhubaneswar, India) USA), Brian Hill (Saint Mary’s College of California, USA), Richard Sohn (Kronos, Inc., Lowell, USA) & Yuan-Sen Ting (Harvard University, “This book is well-written and very readable. The book is a self-consistent USA) introduction to the path integral formalism and no prior knowledge of it is required, although the reader should be familiar with quantum “Sidney Coleman was the master teacher of quantum field theory. All of mechanics. This book is an excellent guide for the reader who wants a us who knew him became his students and disciples. Sidney’s legendary good and detailed introduction to the path integral and most of its important course remains fresh and bracing, because he chose his topics with a sure application in physics. I especially recommend it for graduate students in feel for the essential, and treated them with elegant economy.” theoretical physics and for researchers who want to be introduced to the Frank Wilczek powerful path integral methods.” Nobel Laureate in Physics 2004 Mathematical Reviews 1196pp Dec 2018 -
Physics 616 Quantum Field Theory I(3 Credits)
Physics 616 Quantum Field Theory I (3 credits) Fall 2011 Instructor: Prof. Michael Eides 279 Chem.-Phys. Bldg. Phone 257-3997 E-mail: [email protected] Office hours: Tuesday, 2:00-4:00 pm, or by appointment. Class meets Tuesday, Thursday, 9:30-10:45 am (CP 183). There will be no classes on Thursday, November 24 (Thanksgiving). Grading: I will give you home assignments approximately every 10 days. Your homework will be graded (40 points). Solutions to all problems will be placed in the library. I advice you to read my solutions with great care. If you have any questions about my solutions (as I expect you would), you are welcome in my office for discussion. I encourage you to discuss the homework together, and even to work on it together. However, you should write up your homework separately. Identical solutions would not earn any points. There will be no midterm exam. There will be a take-home final exam due Friday, December 12 (60 points). It could happen that I will change my mind and ask each of you to prepare a short talk (20-25 min) instead of the final exam. Student Evaluations: Course evaluations are an important (and mandatory!) component of our De- partment’s instructional program. The evaluation window for Fall 2011 will open on Wednesday, November 16, and close on Wednesday, Wednesday, December 7th. To access the system during this time, simply go to ”Courses” on the A&S Departmental Website page, and click on the link for Course Evaluations; then follow the instructions. -
Einstein's Equations for Spin 2 Mass 0 from Noether's Converse Hilbertian
Einstein’s Equations for Spin 2 Mass 0 from Noether’s Converse Hilbertian Assertion October 4, 2016 J. Brian Pitts Faculty of Philosophy, University of Cambridge [email protected] forthcoming in Studies in History and Philosophy of Modern Physics Abstract An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether’s 1918 paper developed Hilbert’s and Klein’s reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a “curl” term with identically zero divergence. Noether proved a converse “Hilbertian assertion”: such “improper” conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations as- suming the absence of negative-energy degrees of freedom (“ghosts”) for stability, along with universal coupling: all energy-momentum including gravity’s serves as a source for gravity. Those assumptions (all but) imply (for 0 graviton mass) that the energy-momentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld’s stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form. The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. -
Guest Editorial: Truth, Beauty, and Supergravity Stanley Deser
Guest Editorial: Truth, beauty, and supergravity Stanley Deser Citation: American Journal of Physics 85, 809 (2017); doi: 10.1119/1.4994807 View online: http://dx.doi.org/10.1119/1.4994807 View Table of Contents: http://aapt.scitation.org/toc/ajp/85/11 Published by the American Association of Physics Teachers Articles you may be interested in Entanglement isn't just for spin American Journal of Physics 85, 812 (2017); 10.1119/1.5003808 Three new roads to the Planck scale American Journal of Physics 85, 865 (2017); 10.1119/1.4994804 A demonstration of decoherence for beginners American Journal of Physics 85, 870 (2017); 10.1119/1.5005526 The geometry of relativity American Journal of Physics 85, 683 (2017); 10.1119/1.4997027 The gravitational self-interaction of the Earth's tidal bulge American Journal of Physics 85, 663 (2017); 10.1119/1.4985124 John Stewart Bell and Twentieth-Century Physics: Vision and Integrity American Journal of Physics 85, 880 (2017); 10.1119/1.4983117 GUEST EDITORIAL Guest Editorial: Truth, beauty, and supergravity (Received 9 June 2017; accepted 28 June 2017) [http://dx.doi.org/10.1119/1.4994807] I begin with a warning: theoretical physics is an edifice Dirac equation governing the behavior of electrons—as well built over the centuries by some of mankind’s greatest minds, as all the other leptons and quarks, hence also our protons using ever more complicated and sophisticated concepts and and neutrons. Indeed, it is perhaps one of our three most mathematics to cover phenomena on scales billions of times beautiful equations, along with Maxwell’s and Einstein’s! It removed—in directions both bigger and smaller—from our came full-blown from the head of one of the true greats of human dimensions, where our simple intuition or primitive the last century, and instantly divided all particles into two language cannot pretend to have any validity. -
Gustaaj C. Cornelis It States the Question Why the Universe Seems To
Philosophica 63 (1999, 1) pp. 7-17 INFLATION. WHERE DID THAT COME FROM? GustaaJ C. Cornelis 1. Introduction It would have been perfect. Empirical data generate theoretical problems (the so-called cosmological paradoxes) and induce a crisis in scientific thinking, i.e. cosmology. A revolution occurs and a new paradigm, in casu big bang cosmology annex inflation theory (the idea that the universe grew exponentially in a split second) emerges. Did the search for dark matter generate the flatness problem, and, subsequently, did the flatness problem lead to inflation theory, did inflation theory solve the flatness paradox, and did it become the new paradigm? Unfortunately, this train of thought cannot be substantiated. So where did the 'ridiculous' idea of iIiflation come from? 2. The paradoxes During the sixties and seventies the so-called cosmological paradoxes came forth, known as the horizon-problem, the flatness-problem and the smoothness-problem. The last one originated out of the first. In literature, these problems were treated as genuine cosmological paradoxes, although - as will be shown - only one can be proven to be a genuine paradox. 2.1. The horizon-problem In 1969 Charles Misner presented the horizon-paradox (Misner, 1969). It states the question why the universe seems to be more uniform than can be explained through thermodynamical processes. Misner acknowledged 8 GUSTAAF C. CORNELIS the fact that the universe could only have a more or less equal distribution of matter and temperature if all parts could 'communicate' with each other at a certain time in the past - given, of course, that the universe did not originate out of a 'perfect' singularity. -
Personal Recollections of the Early Days Before and After the Birth of Supergravity
Personal recollections of the early days before and after the birth of Supergravity Peter van Nieuwenhuizen I March 29, 1976: Dan Freedman, Sergio Ferrara and I submit first paper on Supergravity to Physical Review D. I April 28: Stanley Deser and Bruno Zumino: elegant reformulation that stresses the role of torsion. I June 2, 2016 at 1:30pm: 5500 papers with Supergravity in the title have appeared, and 15000 dealing with supergravity. I Supergravity has I led to the AdS/CFT miracle, and I made breakthroughs in longstanding problems in mathematics. I Final role of supergravity? (is it a solution in search of a problem?) I 336 papers in supergravity with 126 collaborators I Now: many directions I can only observe in awe from the sidelines I will therefore tell you my early recollections and some anecdotes. I will end with a new research program that I am enthusiastic about. In 1972 I was a Joliot Curie fellow at Orsay (now the Ecole Normale) in Paris. Another postdoc (Andrew Rothery from England) showed me a little book on GR by Lawden.1 I was hooked. That year Deser gave lectures at Orsay on GR, and I went with him to Brandeis. In 1973, 't Hooft and Veltman applied their new covariant quantization methods and dimensional regularization to pure gravity, using the 't Hooft lemma (Gilkey) for 1-loop divergences and the background field formalism of Bryce DeWitt. They found that at one loop, pure gravity was finite: 1 2 2 ∆L ≈ αRµν + βR = 0 on-shell. But what about matter couplings? 1\An Introduction to Tensor Calculus and Relativity". -
Chern-Simons Terms As an Example of the Relations Between Mathematics and Physics
PUBLICATIONS MATHÉMATIQUES DE L’I.H.É.S. STANLEY DESER Chern-Simons terms as an example of the relations between mathematics and physics Publications mathématiques de l’I.H.É.S., tome S88 (1998), p. 47-51 <http://www.numdam.org/item?id=PMIHES_1998__S88__47_0> © Publications mathématiques de l’I.H.É.S., 1998, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions géné- rales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou im- pression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ CHERN-SIMONS TERMS AS AN EXAMPLE OF THE RELATIONS BETWEEN MATHEMATICS AND PHYSICS by STANLEY DESER The inevitability of Chern-Simons terms in constructing a variety of physical models, and the mathematical advances they in turn generate, illustrate the unexpected but profound interactions between the two disciplines. 1 begin with warmest greetings to the Institut des Hautes Études Scientifiques (IHÉS) on the occasion of its 40th birthday, and look forward to its successes in the years to come. My own association dates back to its early days in 1966-67 and it has continued fruitfully ever since. The IHÉS represents a unique synthesis between Mathematics and Physics, as empha- sized by this volume’s title. I propose to illustrate this synthesis through a particular set of examples, Chern-Simons "effects" in physics. -
Notes from Sidney Coleman's Physics 253A
Notes from Sidney Coleman’s Physics 253a Sidney Coleman∗ Harvard, Fall 1985-1986 semester† ∗typeset by Bryan Gin-ge Chen and Ting Yuan Sen from scans of the handwritten notes of Brian Hill † LATEX version of March 14, 2011 1 0.Preface NotesfromSidneyColeman’sPhysics253a 2 0 Preface It’s unexpected and heart-warming to be asked by Bryan Chen to write something about these notes, 25 years after taking them. I was the teaching assistant for Sidney’s quantum field theory course for three years. In the first year, I sat in, because frankly, I hadn’t learned quantum field theory well enough the first time that I took it. When I have the good fortune to hear a really good lecturer, I often re-copy my notes, preferably the evening on the day that I took them. Once in a while, students would miss a class, and then ask me if they could look at my notes. At some point, the requests started happening enough that it was suggested that a copy be put on reserve in the Harvard physics library. From there, copies of the notes just kept spreading. Sidney once expressed disappointment about the spread of the notes. For one thing, I even wrote down some of his anecdotes and jokes, and that made it less fun for him to re-tell them. For another, he wrote Aspects of Symmetry which shared a lot of material with what he taught in Physics 253b. He may have had in mind that he would write a field theory book as a companion volume.