DOCSLIB.ORG

PDF Document

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
PDF Document String theorists win Dirac Medal P-2 Is string theory a theory or a framework? What impacts will the Large Hadron Collider experiments have on the field? ICTP Dirac Medallists Juan Martín Maldacena, Joseph Polchinski and Cumrun Vafa share their insights on this proposal for a unified description of fundamental interactions in nature, and also describe what they find most exciting about string theory • • • ICTP celebrates Year of Darwin P-5 The link between physics and human evolution may not seem immediately obvious. Yet, the tools of modern physics can date human evolution and dispersal accurately. The tools and techniques used to pinpoint the age of human bones and teeth were the subject of an ICTP exhibit and lecture series held in conjunction with UNESCO’s symposium on Darwin, Evolution and Science • • • Focus on Africa CENTREFOLD ICTP has a long tradition of scientific capacity-building in Africa. Registrazione presso il Tribunale di Trieste n. 1044 del 01.03.2002 | Contiene Inserto Redazionale n. 1044 del 01.03.2002 | Contiene Inserto di Trieste il Tribunale presso Registrazione Over the last few decades, ICTP has supported numerous activities throughout the continent, including training programmes, networks and the establishment of affiliate centres. In Trieste, ICTP has welcomed more than 10,000 African visitors since 1970, providing advanced research and NEWSNEWS training opportunities unavailable to scientists in their home countries • • • NEW SCIENCE FOR CLEAN ENERGY (P-6) | EXPERIMENTAL PLASMA PHYSICS n°127 AT ICTP (P-7) | SNO DIRECTOR VISITS ICTP (P-8) | RESEARCH NEWS BRIEFS Spring/Summer 2009 (P-12) | NEW STAFF (P-16) | ACHIEVEMENTS/PRIZES (P-17) from ICTP Poste Italiane S.p.A. - Spedizione in Abbonamento Postale - D.L. 353/2003 (conv. in L. 27/02/2004 n° 46) art. 1, comma 2, DCB Trieste in L. 27/02/2004 n° 46) art. 1, comma - D.L. 353/2003 (conv. Postale S.p.A. - Spedizione in Abbonamento Italiane Poste NEWS from ICTP 127 + Cumrun Vafa received the Dirac Medal in June 2009, Noted physicists during the Summer School on Particle Physics in the LHC Era. ++ Juan Martín Maldacena and awarded Joseph Polchinski at the Dirac Medal 2008 award ceremony. Dirac Medals +++ Close-up of Dirac Medal. + ++ +++ are very primitive and more like a framework. Do you think string theory will ever be accepted as widely as the theory of general relativity? What would it take for that to happen? Maldacena: What is necessary is CEREMONY HONOURS WORK RELATED TO STRING THEORY that some prediction of the theory is experimentally verified. If that ICTP presented its Dirac Medal to the winners of the 2008 prize at a ceremony happens, it would then be accepted held on 26 March at the Centre. The Dirac Medal is given in honour of P.A.M. widely. Dirac, one of the greatest physicists of the 20th century and a staunch friend of ICTP, Polchinski: This question has two to scientists who have made significant parts: is it the right theory, and will DIRAC MEDALS contributions to physics. we know? For the first part, I feel The recipients—Juan Martín Maldacena strongly that it is the right theory. of the Institute for Advanced Study, More precisely, since it is incomplete, Princeton; Joseph Polchinski of the Kavli it is headed toward the right theory. Institute for Theoretical Physics, University of California at Santa Barbara; Part of the reason for this belief and Cumrun Vafa of Harvard University—were honoured for their substantial is theoretical: it ties together so contributions to string theory, a proposal for a unified description of many things that we already know. fundamental interactions in nature. For example, there is a theory of News from ICTP posed a number of questions related to string theory to the quantum gravity hidden in the three medallists; their thoughts on the theory are presented below. strong nuclear force, and this turns out to be string theory. Also, the Is string theory a theory or a framework? dark energy is an experimental hint, it was predicted by Steven Weinberg Maldacena: It is a theory under construction. We do not yet know what the based on assumptions that seem to fundamental principles underlying it are. follow from string theory. Will we ever know? In the long Polchinski: I think it is a theory because all signs are that its equations are term I am an optimist, one learns unique. But these equations have many solutions, so in a way it behaves as surprising things that were a framework. This property, having few equations with many solutions, is completely unexpected. essential to the nature of physics, which explains many phenomena in terms of a few principles. String theory is perhaps the extreme example of this. Vafa: Yes, I believe it will. It is hard to predict exactly how this will Vafa: It is in some aspects a theory and in others a framework. There are happen, but the richness of string pieces of string theory that are quite well developed, and there are parts which theory and the connections it already 3 has made with general relativity, in the next few years, but they seem true at LHC. We are fortunate to be quantum field theory and other areas to be a narrow class of possibilities. living in exciting times for particle of physics make this unavoidable. One possibility is that the string physics! scale is very low, of the order of the Are the Large Hadron Collider energies that will be explored at What is the most exciting aspect (LHC) experiments likely to have the LHC. The other is that cosmic of string theory for you? a fundamental impact on the field fundamental strings were produced of string theory? in the beginning of the big bang and Maldacena: It is the possibility of have survived until now. describing the initial instants of the Maldacena: Yes, discovering the It might be possible that big bang. We do not yet understand new layer of physics will probably be somebody understands the theory the theory well enough to say very useful for guiding us towards better and comes up with a whether it does indeed describe the correct theory. Understanding prediction that applies to a wider it, but this is the most exciting how electroweak symmetry is spectrum of possibilities. prospect and a strong motivation for broken is very important. Questions Finally, I should say that string developing the theory further. that will be answered are: Is there theory could be easily falsified by any a natural explanation for the scale experiment that shows a departure Polchinski: The way that it connects at which electroweak symmetry is from quantum mechanics. Since things. An example is the way that broken? Do we have supersymmetry string theory is based on quantum the strong nuclear force and gravity at this scale? mechanics, any violation of the usual are dual, just different classical rules of quantum mechanics by any limits of a single quantum theory. Polchinski: There are some possible tabletop experiment would rule out The duality between black holes smoking guns—extra dimensions string theory. and strongly interacting plasmas and black holes—but these are long is a striking illustration of this. shots. But whatever we learn will Polchinski: I have been studying Seemingly distant parts of physics be important, since there are so the possibility of cosmic strings, end up being closely related, in many possibilities now and a real which would have expanded with the surprising ways. mystery as to what will be seen. The universe and today might be seen strongest candidate, supersymmetry, through their gravitational effects. Vafa: The interconnection between is very interesting and is an Again, they are present in some ideas and the unifying framework important part of string theory, so if solutions but not all, so they are not a that string theory provides for the LHC has enough energy to find it firm prediction. But if they are found, physics is very exciting. Also, we are in good shape. they will be a huge new window into how one corner of string theory high-energy physics. transitions to another seamlessly Vafa: I believe it will, and I am through string dualities is quite hopeful that it would refine our Vafa: Together with my student beautiful. understanding of string theory. LHC Jonathan Heckman and with many is bound to have a lasting impact other collaborators, we have come How can fundamental science on the whole field of high-energy up with a framework from string contribute to the growth of physics. theory with very specific predictions developing countries? for particle physics and what LHC Can you give an example of a may find. This includes the mass of Maldacena: Researchers in basic prediction of string theory that supersymmetric particles we may areas of science are a resource for might be experimentally verified discover at LHC, as well as specific people who work on more applied in coming years? candidates for dark matter. We also areas, which would be the ones most have predictions for neutrino physics crucial for development. I do think Maldacena: We would have to be which would be interesting to verify that applied research is best done by lucky to have any verification in the in the near future experiments. I am the private sector, which has a better near future. There are scenarios hopeful that with some luck we may sense of what is most economically where verification would be possible see some of these predictions proven viable. NEWS from ICTP 127 Polchinski: I think that all people wonder about the nature of things, how they began and what is at the Dirac bottom of everything.
Load more

Recommended publications
  • String Theory. Volume 1, Introduction to the Bosonic String
    This page intentionally left blank String Theory, An Introduction to the Bosonic String The two volumes that comprise String Theory provide an up-to-date, comprehensive, and pedagogic introduction to string theory. Volume I, An Introduction to the Bosonic String, provides a thorough introduction to the bosonic string, based on the Polyakov path integral and conformal field theory. The first four chapters introduce the central ideas of string theory, the tools of conformal field theory and of the Polyakov path integral, and the covariant quantization of the string. The next three chapters treat string interactions: the general formalism, and detailed treatments of the tree-level and one loop amplitudes. Chapter eight covers toroidal compactification and many important aspects of string physics, such as T-duality and D-branes. Chapter nine treats higher-order amplitudes, including an analysis of the finiteness and unitarity, and various nonperturbative ideas. An appendix giving a short course on path integral methods is also included. Volume II, Superstring Theory and Beyond, begins with an introduction to supersym- metric string theories and goes on to a broad presentation of the important advances of recent years. The first three chapters introduce the type I, type II, and heterotic superstring theories and their interactions. The next two chapters present important recent discoveries about strongly coupled strings, beginning with a detailed treatment of D-branes and their dynamics, and covering string duality, M-theory, and black hole entropy. A following chapter collects many classic results in conformal field theory. The final four chapters are concerned with four-dimensional string theories, and have two goals: to show how some of the simplest string models connect with previous ideas for unifying the Standard Model; and to collect many important and beautiful general results on world-sheet and spacetime symmetries.
    [Show full text]
  • 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.
    [Show full text]
  • Subnuclear Physics: Past, Present and Future
    Subnuclear Physics: Past, Present and Future International Symposium 30 October - 2 November 2011 – The purpose of the Symposium is to discuss the origin, the status and the future of the new frontier of Physics, the Subnuclear World, whose first two hints were discovered in the middle of the last century: the so-called “Strange Particles” and the “Resonance #++”. It took more than two decades to understand the real meaning of these two great discoveries: the existence of the Subnuclear World with regularities, spontaneously plus directly broken Symmetries, and totally unexpected phenomena including the existence of a new fundamental force of Nature, called Quantum ChromoDynamics. In order to reach this new frontier of our knowledge, new Laboratories were established all over the world, in Europe, in USA and in the former Soviet Union, with thousands of physicists, engineers and specialists in the most advanced technologies, engaged in the implementation of new experiments of ever increasing complexity. At present the most advanced Laboratory in the world is CERN where experiments are being performed with the Large Hadron Collider (LHC), the most powerful collider in the world, which is able to reach the highest energies possible in this satellite of the Sun, called Earth. Understanding the laws governing the Space-time intervals in the range of 10-17 cm and 10-23 sec will allow our form of living matter endowed with Reason to open new horizons in our knowledge. Antonino Zichichi Participants Prof. Werner Arber H.E. Msgr. Marcelo Sánchez Sorondo Prof. Guido Altarelli Prof. Ignatios Antoniadis Prof. Robert Aymar Prof. Rinaldo Baldini Ferroli Prof.
    [Show full text]
  • Stephen Hawking: 'There Are No Black Holes' Notion of an 'Event Horizon', from Which Nothing Can Escape, Is Incompatible with Quantum Theory, Physicist Claims
    NATURE | NEWS Stephen Hawking: 'There are no black holes' Notion of an 'event horizon', from which nothing can escape, is incompatible with quantum theory, physicist claims. Zeeya Merali 24 January 2014 Artist's impression VICTOR HABBICK VISIONS/SPL/Getty The defining characteristic of a black hole may have to give, if the two pillars of modern physics — general relativity and quantum theory — are both correct. Most physicists foolhardy enough to write a paper claiming that “there are no black holes” — at least not in the sense we usually imagine — would probably be dismissed as cranks. But when the call to redefine these cosmic crunchers comes from Stephen Hawking, it’s worth taking notice. In a paper posted online, the physicist, based at the University of Cambridge, UK, and one of the creators of modern black-hole theory, does away with the notion of an event horizon, the invisible boundary thought to shroud every black hole, beyond which nothing, not even light, can escape. In its stead, Hawking’s radical proposal is a much more benign “apparent horizon”, “There is no escape from which only temporarily holds matter and energy prisoner before eventually a black hole in classical releasing them, albeit in a more garbled form. theory, but quantum theory enables energy “There is no escape from a black hole in classical theory,” Hawking told Nature. Peter van den Berg/Photoshot and information to Quantum theory, however, “enables energy and information to escape from a escape.” black hole”. A full explanation of the process, the physicist admits, would require a theory that successfully merges gravity with the other fundamental forces of nature.
    [Show full text]
  • Inflation, Large Branes, and the Shape of Space
    Inflation, Large Branes, and the Shape of Space Brett McInnes National University of Singapore email: [email protected] ABSTRACT Linde has recently argued that compact flat or negatively curved spatial sections should, in many circumstances, be considered typical in Inflationary cosmologies. We suggest that the “large brane instability” of Seiberg and Witten eliminates the negative candidates in the context of string theory. That leaves the flat, compact, three-dimensional manifolds — Conway’s platycosms. We show that deep theorems of Schoen, Yau, Gromov and Lawson imply that, even in this case, Seiberg-Witten instability can be avoided only with difficulty. Using a specific cosmological model of the Maldacena-Maoz type, we explain how to do this, and we also show how the list of platycosmic candidates can be reduced to three. This leads to an extension of the basic idea: the conformal compactification of the entire Euclidean spacetime also has the topology of a flat, compact, four-dimensional space. arXiv:hep-th/0410115v2 19 Oct 2004 1. Nearly Flat or Really Flat? Linde has recently argued [1] that, at least in some circumstances, we should regard cosmological models with flat or negatively curved compact spatial sections as the norm from an Inflationary point of view. Here we wish to argue that cosmic holography, in the novel form proposed by Maldacena and Maoz [2], gives a deep new interpretation of this idea, and also sharpens it very considerably to exclude the negative case. This focuses our attention on cosmological models with flat, compact spatial sections. Current observations [3] show that the spatial sections of our Universe [as defined by observers for whom local isotropy obtains] are fairly close to being flat: the total density parameter Ω satisfies Ω = 1.02 0.02 at 95% confidence level, if we allow the imposition ± of a reasonable prior [4] on the Hubble parameter.
    [Show full text]
  • Field Theory Insight from the Ads/CFT Correspondence
    Field theory insight from the AdS/CFT correspondence Daniel Z.Freedman1 and Pierre Henry-Labord`ere2 1Department of Mathematics and Center for Theoretical Physics Massachusetts Institute of Technology, Cambridge, MA 01239 E-mail: [email protected] 2LPT-ENS, 24, rue Lhomond F-75231 Paris cedex 05, France E-mail: [email protected] ABSTRACT A survey of ideas, techniques and results from d=5 supergravity for the conformal and mass-perturbed phases of d=4 N =4 Super-Yang-Mills theory. arXiv:hep-th/0011086v2 29 Nov 2000 1 Introduction The AdS/CF T correspondence [1, 20, 11, 12] allows one to calculate quantities of interest in certain d=4 supersymmetric gauge theories using 5 and 10-dimensional supergravity. Mirac- ulously one gets information on a strong coupling limit of the gauge theory– information not otherwise available– from classical supergravity in which calculations are feasible. The prime example of AdS/CF T is the duality between =4 SYM theory and D=10 N Type IIB supergravity. The field theory has the very special property that it is ultraviolet finite and thus conformal invariant. Many years of elegant work on 2-dimensional CF T ′s has taught us that it is useful to consider both the conformal theory and its deformation by relevant operators which changes the long distance behavior and generates a renormalization group flow of the couplings. Analogously, in d=4, one can consider a) the conformal phase of =4 SYM N b) the same theory deformed by adding mass terms to its Lagrangian c) the Coulomb/Higgs phase.
    [Show full text]
  • Anomalies, Dualities, and Topology of D = 6 N = 1 Superstring Vacua
    RU-96-16 NSF-ITP-96-21 CALT-68-2057 IASSNS-HEP-96/53 hep-th/9605184 Anomalies, Dualities, and Topology of D =6 N =1 Superstring Vacua Micha Berkooz,1 Robert G. Leigh,1 Joseph Polchinski,2 John H. Schwarz,3 Nathan Seiberg,1 and Edward Witten4 1Department of Physics, Rutgers University, Piscataway, NJ 08855-0849 2Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030 3California Institute of Technology, Pasadena, CA 91125 4Institute for Advanced Study, Princeton, NJ 08540 Abstract We consider various aspects of compactifications of the Type I/heterotic Spin(32)/Z2 theory on K3. One family of such compactifications in- cludes the standard embedding of the spin connection in the gauge group, and is on the same moduli space as the compactification of arXiv:hep-th/9605184v1 25 May 1996 the heterotic E8 × E8 theory on K3 with instanton numbers (8,16). Another class, which includes an orbifold of the Type I theory re- cently constructed by Gimon and Polchinski and whose field theory limit involves some topological novelties, is on the moduli space of the heterotic E8 × E8 theory on K3 with instanton numbers (12,12). These connections between Spin(32)/Z2 and E8 × E8 models can be demonstrated by T duality, and permit a better understanding of non- perturbative gauge fields in the (12,12) model. In the transformation between Spin(32)/Z2 and E8 × E8 models, the strong/weak coupling duality of the (12,12) E8 × E8 model is mapped to T duality in the Type I theory. The gauge and gravitational anomalies in the Type I theory are canceled by an extension of the Green-Schwarz mechanism.
    [Show full text]
  • Eternal Inflation and Its Implications
    IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 40 (2007) 6811–6826 doi:10.1088/1751-8113/40/25/S25 Eternal inflation and its implications Alan H Guth Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA E-mail: [email protected] Received 8 February 2006 Published 6 June 2007 Online at stacks.iop.org/JPhysA/40/6811 Abstract Isummarizetheargumentsthatstronglysuggestthatouruniverseisthe product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region. PACS numbers: 98.80.cQ, 98.80.Bp, 98.80.Es 1. Introduction: the successes of inflation Since the proposal of the inflationary model some 25 years ago [1–4], inflation has been remarkably successful in explaining many important qualitative and quantitative properties of the universe. In this paper, I will summarize the key successes, and then discuss a number of issues associated with the eternal nature of inflation.
    [Show full text]
  • GSS: Gauge and String Theories
    GSS: Gauge and String Theories S. Bellucci (Resp.), S. Ferrara (Ass.), S. Krivonos (Osp.), A. Sutulin (Bors. PD), B.N. Tiwari (Ospite), A. Yeranyan (Bors. Fermi Institute) Research Activity S. Ferrara investigated different aspects of black-hole physics, which include a classification of charge- orbits for extremal single-center black holes and first-order flows of extremal black holes with different BPS properties. He also investigated some aspects of multi-center black holes and, in particular, the classification of two-center orbits and first order flows for multi-center composites. He studied several aspects of supersymmetry breaking. Applications to Particle Physics or to inflation rest on N=1 spontaneously broken supergravity where some multiplets mediate supersymmetry breaking while others accommodate the inflaton. The supersymmetric extension of the Starobinsky model depends on the off-shell formulation of the local supersymmetry algebra. This allows one to show the equivalence of this higher curvature theory to a standard Einstein supergravity. Depending on the chosen formulation the model corresponds to supergravity coupled either to two massive chiral multiplets, one of which is the goldstino multiplet, or to a massive vector multiplet. He also introduced a set of minimal models, where the inflaton sector is described by a single scalar field (with D term and Fayet-Iliopoulos term generating potential), unlike in models based on chiral multiplets based on an F-term potential. In minimal models the scalaron is dual to the inflaton, and being the member of a massive vector multiplet, it is the superpartner of the Stueckelberg field. Subsequently, replacing the Goldstino multiplet with its non-linear realization via a nilpotent superfield, he arrived at a new universal Volkov-Akulov-Starobinsky Supergravity.
    [Show full text]
  • Global Program
    PROGRAM Monday morning, July 13th La Sapienza Roma - Aula Magna 09:00 - 10:00 Inaugural Session Chairperson: Paolo de Bernardis Welcoming addresses Remo Ruffini (ICRANet), Yvonne Choquet-Bruhat (French Académie des Sciences), Jose’ Funes (Vatican City), Ricardo Neiva Tavares (Ambassador of Brazil), Sargis Ghazaryan (Ambassador of Armenia), Francis Everitt (Stanford University) and Chris Fryer (University of Arizona) Marcel Grossmann Awards Yakov Sinai, Martin Rees, Sachiko Tsuruta, Ken’Ichi Nomoto, ESA (acceptance speech by Johann-Dietrich Woerner, ESA Director General) Lectiones Magistrales Yakov Sinai (Princeton University) 10:00 - 10:35 Deterministic chaos Martin Rees (University of Cambridge) 10:35 - 11:10 How our understanding of cosmology and black holes has been revolutionised since the 1960s 11:10 - 11:35 Group Picture - Coffee Break Gerard 't Hooft (University of Utrecht) 11:35 - 12:10 Local Conformal Symmetry in Black Holes, Standard Model, and Quantum Gravity Plenary Session: Mathematics and GR Katarzyna Rejzner (University of York) 12:10 - 12:40 Effective quantum gravity observables and locally covariant QFT Zvi Bern (UCLA Physics & Astronomy) 12:40 - 13:10 Ultraviolet surprises in quantum gravity 14:30 - 18:00 Parallel Session 18:45 - 20:00 Stephen Hawking (teleconference) (University of Cambridge) Public Lecture Fire in the Equations Monday afternoon, July 13th Code Classroom Title Chairperson AC2 ChN1 MHD processes near compact objects Sergej Moiseenko FF Extended Theories of Gravity and Quantum Salvatore Capozziello, Gabriele AT1 A Cabibbo Cosmology Gionti AT3 A FF3 Wormholes, Energy Conditions and Time Machines Francisco Lobo Localized selfgravitating field systems in the AT4 FF6 Dmitry Galtsov, Michael Volkov Einstein and alternatives theories of gravity BH1:Binary Black Holes as Sources of Pablo Laguna, Anatoly M.
    [Show full text]
  • 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]
  • Geometric Approaches to Quantum Field Theory
    GEOMETRIC APPROACHES TO QUANTUM FIELD THEORY A thesis submitted to The University of Manchester for the degree of Doctor of Philosophy in the Faculty of Science and Engineering 2020 Kieran T. O. Finn School of Physics and Astronomy Supervised by Professor Apostolos Pilaftsis BLANK PAGE 2 Contents Abstract 7 Declaration 9 Copyright 11 Acknowledgements 13 Publications by the Author 15 1 Introduction 19 1.1 Unit Independence . 20 1.2 Reparametrisation Invariance in Quantum Field Theories . 24 1.3 Example: Complex Scalar Field . 25 1.4 Outline . 31 1.5 Conventions . 34 2 Field Space Covariance 35 2.1 Riemannian Geometry . 35 2.1.1 Manifolds . 35 2.1.2 Tensors . 36 2.1.3 Connections and the Covariant Derivative . 37 2.1.4 Distances on the Manifold . 38 2.1.5 Curvature of a Manifold . 39 2.1.6 Local Normal Coordinates and the Vielbein Formalism 41 2.1.7 Submanifolds and Induced Metrics . 42 2.1.8 The Geodesic Equation . 42 2.1.9 Isometries . 43 2.2 The Field Space . 44 2.2.1 Interpretation of the Field Space . 48 3 2.3 The Configuration Space . 50 2.4 Parametrisation Dependence of Standard Approaches to Quan- tum Field Theory . 52 2.4.1 Feynman Diagrams . 53 2.4.2 The Effective Action . 56 2.5 Covariant Approaches to Quantum Field Theory . 59 2.5.1 Covariant Feynman Diagrams . 59 2.5.2 The Vilkovisky–DeWitt Effective Action . 62 2.6 Example: Complex Scalar Field . 66 3 Frame Covariance in Quantum Gravity 69 3.1 The Cosmological Frame Problem .
    [Show full text]