DOCSLIB.ORG

Field Theory and Particle Physics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

V Jorge Andre Swieca Summer School Field Theory and Particle Physics Campos do Jordão, Brazil f. 8-21 January 1989 Editors O.J.P. Éboli, 17. Gomes and A. Santoro World Scientific Singapore • New Jersey • London • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd., P O Box 128, Fairer Road, Singapore 9128 USA office: 687 HatlweU Street, Teaneck, NJ G7666 UK office: 73 Lynton Mead, Totteridge, London N20 8DH Library of Congress Cataloging -in-Publication data is available. FIELD THEORY AND PARTICLE PHYSICS Copyright © 1990 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photo- copying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. ISBN 981-02-0057-9 Printed in Singapore by JBW Printer» & Binders Pte. Ltd. PREFACE The V Jorge André Swieca Summer School was held at Campos do Jordão, a small village near São Paulo, from January 8 to 21, 1989. This event provided a series of lectures and seminars delivered by invited speakers. These Proceedings contains the lectures notes of the topics covered during the school. The first part of the book collects the material devoted to quantum field the- ory. There were four courses on methods in Field Theory: H. 0. Girotti lectured on constrained dynamics, R. Jackiw on the Schrõdinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson- Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformai Field Theory: I. Todorov focused on the problem of construction and classification of conformai field theories. Lattice models, two-dimensional 5 ma- trices and conformai field theory were looked from the unifying perspective of the .Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introdution to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gêrbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions. We would like to thank everybody who contributed for the success of the V Jorge Andre Swieca Summer School. Very special thanks are due to the lecturers who gave a very nice set of lectures and shared their knowledge and time with the participants. The School would not have been possible without the financial support from the following institutions: CLAF, SBF, FAPESP, ICTP (Trieste), FAPERJ, CNPq, CAPES, FINEP, IBM, FERMILAB and the University of Sio Paulo. O.J.P. Éboli M. Gomes A. Santoro Lecturers and Topics G. Cohen-Tannoudji (Saclay) QCD and Hadronic Strings H . 0. Girotti (UFRGS) Classical and Quantum Dynamics of Constrained Systems D. Green (Fermilab) pp Collider Physics G. Horowitz (Santa Barbara) Introduction to String Field Theory R. Jackiw (MIT) Analysis on Infinite Dimensional Manifolds Schrõdinger Representation for Quantized Fields M. Karowski (ETH) Yang-Baxter Algebra - Integrable Systems - Conformai Quantum Field Theories S.-Young. Pi (BÜ) Quantum Field Theory in Flat Robertson-Walker Space-Time: Functional Schrõdinger Picture E. Predazzi (Turim) Strong Interaction Phenomenology I. Todorov (Sofia) Rational Conformai Theories Involving a U(l) Current Algebra L. Vinet (Montreal) Dynamical Parasupersymmetries in Quantum Mechanics- Berry Connections Seminar speakers P. S. Gerbert (MIT) Gravity in 2 + 1 Dimensions V. Kurak (IFUSP) Parafcrmioníc Conformai Field Theory F. Schaposnick (La Plata) Topological Field Theories and Two Dimensional Instantons Vtt Participants AbdaJla, E. IFUSP Abdalla, M.C.B. IFT UNESP Almeida, C.A.S. CBPF Almeida, L.D. IFT UNESP Amaral, R.L.P.G. PUCRJ Alves, M.S. ÜFRJ Bazeia Filho, D. UFPB Bedaque, P.S.F. IFUSP Belletato, P. PUCRJ Biancolin, M.M IFUSP Botelho, L.C. UFPA Bouzas, A.O. La Plata Brunelli, J.C. IFUSP Brunetto, S.Q. UNICAMP Brunint, S.A. IFUSP Caldas, P.S.S- IFUSP Carvalho, H.F.de UFRJ Carvalho, L.de C. CBPF Constantinidis, C.P. IFQSC Covolan, R.J.M. UNICAMP Demarco, G.L CAB Dias, S.A. CBPF Ducatti, M.B.G. UFRGS Dutra, A.de S. CBPF Evangelista, L.R. FUEM Ferreira, L.A. IFT UNESP Figueiredo, B.D.B CBPF Foster, A. UFRGS Gerbert, P.S. MIT Gones, J.F. IFT UNESP Gonade, J.R. IFÜSP Hasiran, N.M. CBPF Hickman, I.A.B.e CBPF Kneipp, M.A.C. CBPF Kobe, D. IFT UNESP Kunk, V. IFUSP Kurobart, SM. IFUSP Kõrbde,R. IFQSC Lima, A.F.de IFUSP lira, MB. UC Luanda, J. IEAV-CTA Macedo, A.A.S. PUCRJ Maciel, A. CBPF Magalhães, N.S. IFUSP Mardooes, A.A. UC Moricone, L. PUCRJ MarvuIIc,V. IFUSP Melter J.C. UFR-RJ Mendes, R.dos S. IFUSP Menon, M.J. UNICAMP Menon, M.L.T. UNICAMP Montalvo, J.E.C. IFUSP Moraes Filho, A.Z. IFT UNESP Moreno, E. La Plata IX Nascimento, J.R.S.do ÜFPB Negrini Neto, O. IFUSP Piquini, P.C- IFUSP Pierri.M. CBPF Ramos, R-de O. IFÜSP Ricci, T.S.F. ÜFRGS Ricotta, R.M. IFT ÜNESP Rivefles, Vde 0. IFUSP Rodrigues, R.L. IFT ÜNESP Sabrò,A. PUCRJ Sandoval Junior, L. IFUSP Schaposnik, F. Ia Plata Sigaud Filho, C UFRJ Silva, A.Jda IFUSP Souza, C.F.de UFRJ Souzc, M.M.de UFES Suzuki, A.T. **' " ÜNESP Takamura, F.I. PUCRJ Teotònio Sobrinho, P. I^USP Thomaz, M.T.C.S. UFF Valle, J.L.M. CBPF Vanhecke, F.J. UFRJ Zimmerman, A.H. IFT UNESP CAB: Centro Atômico .e Baríloche, 8400 Baríloche- Rio Negro, Argentina. CBPF: Centro Brasileiro de Pesquisas Físi a», rua Dr. Xavier Sigaud, 150, 2290 Rio de Janeiro, RJ, Brasil. IEAV-CTA: Inst. de Estudos Avançados, C. P- 6044, 12231, São José dos Campos, São Paulo, SP, Brasil. IFQSC: Instituto de Física e Química de São Carlos, C. P. 369,13560 São Carlos, SP, Brasil. IFT-UNESP: Instituto de Física Teórica, Universidade Estadual Paulista, ma Pamplona 145, 01405 São Paulo, SP, Brasil. IFUSP: Instituto de Física, Universidade de São Paulo, C. P. 20516, 01498 São Paulo, SP, Brasil. La Plata: Departamento de Física, Universidad Nacional de La Plata, C. C. 67,1900, La Plata, Argentina. PUCRJ: Departamento de Física, Pontifícia Universiade Católica, C P. 38071, 22453, Rio de Janeiro, RJ, Brasil. UC: Departamento de Física, Universidade do Chile, Ca :11a 54S7, Santiago, Chile UFES: Departamento de Física, Universidade Federal do Espirito Santo, Av. Fernando Ferrari s/n, 29000 Vitória, ES, Brasil. UFF: Instituto de Física, Universidade Federal Fluminense, Outeiro de São João B tista s/n, 24020 Niterói, RJ, Brasil. UFPA: Departamento de Física, Universidade Federal do Pará, C. P. 6S, 6600 Belém, PA, Brasil. UFPB: Departamento de Física, Universidade Federal ca Paraíba, 5S0OO João Pessoa, PB, Brasil. UFRJ: Instituto de Física, Universidade Federal do Rio de Janeiro, C. P. 6852$, 21944 Rio de Janeiro, RJ, Brasil. UFRGS: Instituto de Física, Universidade Federal do Rio Grande do Sul, C. P. 15051, 91500 Porto Alegre, RS, Brasil. UFR-RJ: Departamento de Física, Universidade Federal Rural do Rio de Janeiro, 23460 Itaguaí, RJ, Brasil. UNICAMP: Instituto de Física, Universidade Estadual de Campinas, C. P. 1170, 13100 Campinas, São Paulo, Brasil. XI CONTENTS Preface v Lecturers and Topics vi Participants vii Classical and Quantum Dynamics of Constrained Systems 1 H. 0. Girotti Analysis on Infinite-Dimension Manifolds — Schrõdinger Representation for Quantized Fields 78 R.Jackiw Quantum Field Theory in Flat Robertson-Walker Space-Time: Functional Schrõdinger Picture 144 So-Young Pi Rational Conformai Theories Involving a U(l) Current Algebra 196 Ivan T. Todorov Yang-Baxter Algebra — Integrable Systems — Conformai Quantum Field Theories 246 M. Karowski Dynamical Parasupersymmetries in Quantum Mechanics 291 Stephane Durand and Luc Vinet Introduction to String Field Theory — 315 Gary T. Horowitz pp Collide: Physics 370 Dan Green Strong Interaction Phenomenology 489 Maurice Giffon and Enrico Predazzi QCD and Hadronic Strings 656 Gilles Cohen-Tannoudji XB Topological Field Theories and Two-Dimensional Instantons 683 Fidel A. Schaposnik Gravity in 2 + 1 Dimensions 70S Ph. de Sousa Gerbert Parafermionic Conformai Field Theory 719 V. Kurak Author Index 731 CLASSICAL AND QUANTUM DYKAMICS OF CONSTRAINED SYSTEMS H.O.Cirotti Institute de Física Universidade Federal do Rio Grande do Sul Caixa Postal 15051, 9150C Porto Alegre, RS BRASIL Lectures delivered at the Vth Sinner School Jorge Andre Svieca, Section: Particles and Fields. Campos do Jordão, SP, Brazil (1989). CONTENTS I. CLASSICAL DYNAMICS OF CONSTRAINED SYSTEMS 1.1. Singular Systems. Definition. 1.2. Symmetry Transformations 1.3. Hamiltonian Formulation of Constrained Systems 1.4. Reparametrization Transformations 1.5. Gauge Fixing II. QUANTIZATION OF CONSTRAINED SYSTEMS II. 1. The Dine Bracket Quantization Procedure 11.2. Illustrative Example: Canonical Quantization of a Self-Dual Field Theory 11.3. Functional Quantization 11.4. Quantization of First-Class Systems in Non-Canonical Gauges. BRST Quantization. III. ALTERNATIVE FORMULATIONS OF ANOMALOUS CHIRAL GAUGE THEORIES 111.1. Preliminaries 111.2. The Chiral Schwinger Model 111.3. Canonical Quantization of the Gaugi Invariant Chiral Schwinger Model 111.4. The Fermion Operators of the GNI Chiral Schwinger Model I. CLASSICAL DYNAMICS OF CONSTRAINED SYSTEMS I.I. Singular Systems. Definition In order to treat simultaneously physical systems possessing either a finite or an infinite number of degrees of freedom, we found convenient to introduce the following notation: Q (T), A = 1,...,N, denote the coordinates (or fields) spanning the configuration space of the physical system.
Recommended publications
  • The Five Common Particles

    The Five Common Particles

    The Five Common Particles The world around you consists of only three particles: protons, neutrons, and electrons. Protons and neutrons form the nuclei of atoms, and electrons glue everything together and create chemicals and materials. Along with the photon and the neutrino, these particles are essentially the only ones that exist in our solar system, because all the other subatomic particles have half-lives of typically 10-9 second or less, and vanish almost the instant they are created by nuclear reactions in the Sun, etc. Particles interact via the four fundamental forces of nature. Some basic properties of these forces are summarized below. (Other aspects of the fundamental forces are also discussed in the Summary of Particle Physics document on this web site.) Force Range Common Particles It Affects Conserved Quantity gravity infinite neutron, proton, electron, neutrino, photon mass-energy electromagnetic infinite proton, electron, photon charge -14 strong nuclear force ≈ 10 m neutron, proton baryon number -15 weak nuclear force ≈ 10 m neutron, proton, electron, neutrino lepton number Every particle in nature has specific values of all four of the conserved quantities associated with each force. The values for the five common particles are: Particle Rest Mass1 Charge2 Baryon # Lepton # proton 938.3 MeV/c2 +1 e +1 0 neutron 939.6 MeV/c2 0 +1 0 electron 0.511 MeV/c2 -1 e 0 +1 neutrino ≈ 1 eV/c2 0 0 +1 photon 0 eV/c2 0 0 0 1) MeV = mega-electron-volt = 106 eV. It is customary in particle physics to measure the mass of a particle in terms of how much energy it would represent if it were converted via E = mc2.
  • Fundamentals of Particle Physics

    Fundamentals of Particle Physics

    Fundamentals of Par0cle Physics Particle Physics Masterclass Emmanuel Olaiya 1 The Universe u The universe is 15 billion years old u Around 150 billion galaxies (150,000,000,000) u Each galaxy has around 300 billion stars (300,000,000,000) u 150 billion x 300 billion stars (that is a lot of stars!) u That is a huge amount of material u That is an unimaginable amount of particles u How do we even begin to understand all of matter? 2 How many elementary particles does it take to describe the matter around us? 3 We can describe the material around us using just 3 particles . 3 Matter Particles +2/3 U Point like elementary particles that protons and neutrons are made from. Quarks Hence we can construct all nuclei using these two particles -1/3 d -1 Electrons orbit the nuclei and are help to e form molecules. These are also point like elementary particles Leptons We can build the world around us with these 3 particles. But how do they interact. To understand their interactions we have to introduce forces! Force carriers g1 g2 g3 g4 g5 g6 g7 g8 The gluon, of which there are 8 is the force carrier for nuclear forces Consider 2 forces: nuclear forces, and electromagnetism The photon, ie light is the force carrier when experiencing forces such and electricity and magnetism γ SOME FAMILAR THE ATOM PARTICLES ≈10-10m electron (-) 0.511 MeV A Fundamental (“pointlike”) Particle THE NUCLEUS proton (+) 938.3 MeV neutron (0) 939.6 MeV E=mc2. Einstein’s equation tells us mass and energy are equivalent Wave/Particle Duality (Quantum Mechanics) Einstein E
  • Introduction to Particle Physics

    Introduction to Particle Physics

    SFB 676 – Projekt B2 Introduction to Particle Physics Christian Sander (Universität Hamburg) DESY Summer Student Lectures – Hamburg – 20th July '11 Outline ● Introduction ● History: From Democrit to Thomson ● The Standard Model ● Gauge Invariance ● The Higgs Mechanism ● Symmetries … Break ● Shortcomings of the Standard Model ● Physics Beyond the Standard Model ● Recent Results from the LHC ● Outlook Disclaimer: Very personal selection of topics and for sure many important things are left out! 20th July '11 Introduction to Particle Physics 2 20th July '11 Introduction to Particle PhysicsX Files: Season 2, Episode 233 … für Chester war das nur ein Weg das Geld für das eigentlich theoretische Zeugs aufzubringen, was ihn interessierte … die Erforschung Dunkler Materie, …ähm… Quantenpartikel, Neutrinos, Gluonen, Mesonen und Quarks. Subatomare Teilchen Die Geheimnisse des Universums! Theoretisch gesehen sind sie sogar die Bausteine der Wirklichkeit ! Aber niemand weiß, ob sie wirklich existieren !? 20th July '11 Introduction to Particle PhysicsX Files: Season 2, Episode 234 The First Particle Physicist? By convention ['nomos'] sweet is sweet, bitter is bitter, hot is hot, cold is cold, color is color; but in truth there are only atoms and the void. Democrit, * ~460 BC, †~360 BC in Abdera Hypothesis: ● Atoms have same constituents ● Atoms different in shape (assumption: geometrical shapes) ● Iron atoms are solid and strong with hooks that lock them into a solid ● Water atoms are smooth and slippery ● Salt atoms, because of their taste, are sharp and pointed ● Air atoms are light and whirling, pervading all other materials 20th July '11 Introduction to Particle Physics 5 Corpuscular Theory of Light Light consist out of particles (Newton et al.) ↕ Light is a wave (Huygens et al.) ● Mainly because of Newtons prestige, the corpuscle theory was widely accepted (more than 100 years) Sir Isaac Newton ● Failing to describe interference, diffraction, and *1643, †1727 polarization (e.g.
  • Off-Shell Interactions for Closed-String Tachyons

    Off-Shell Interactions for Closed-String Tachyons

    Preprint typeset in JHEP style - PAPER VERSION hep-th/0403238 KIAS-P04017 SLAC-PUB-10384 SU-ITP-04-11 TIFR-04-04 Off-Shell Interactions for Closed-String Tachyons Atish Dabholkarb,c,d, Ashik Iqubald and Joris Raeymaekersa aSchool of Physics, Korea Institute for Advanced Study, 207-43, Cheongryangri-Dong, Dongdaemun-Gu, Seoul 130-722, Korea bStanford Linear Accelerator Center, Stanford University, Stanford, CA 94025, USA cInstitute for Theoretical Physics, Department of Physics, Stanford University, Stanford, CA 94305, USA dDepartment of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India E-mail:[email protected], [email protected], [email protected] Abstract: Off-shell interactions for localized closed-string tachyons in C/ZN super- string backgrounds are analyzed and a conjecture for the effective height of the tachyon potential is elaborated. At large N, some of the relevant tachyons are nearly massless and their interactions can be deduced from the S-matrix. The cubic interactions be- tween these tachyons and the massless fields are computed in a closed form using orbifold CFT techniques. The cubic interaction between nearly-massless tachyons with different charges is shown to vanish and thus condensation of one tachyon does not source the others. It is shown that to leading order in N, the quartic contact in- teraction vanishes and the massless exchanges completely account for the four point scattering amplitude. This indicates that it is necessary to go beyond quartic inter- actions or to include other fields to test the conjecture for the height of the tachyon potential. Keywords: closed-string tachyons, orbifolds.
  • Introductory Lectures on Quantum Field Theory

    Introductory Lectures on Quantum Field Theory

    Introductory Lectures on Quantum Field Theory a b L. Álvarez-Gaumé ∗ and M.A. Vázquez-Mozo † a CERN, Geneva, Switzerland b Universidad de Salamanca, Salamanca, Spain Abstract In these lectures we present a few topics in quantum field theory in detail. Some of them are conceptual and some more practical. They have been se- lected because they appear frequently in current applications to particle physics and string theory. 1 Introduction These notes are based on lectures delivered by L.A.-G. at the 3rd CERN–Latin-American School of High- Energy Physics, Malargüe, Argentina, 27 February–12 March 2005, at the 5th CERN–Latin-American School of High-Energy Physics, Medellín, Colombia, 15–28 March 2009, and at the 6th CERN–Latin- American School of High-Energy Physics, Natal, Brazil, 23 March–5 April 2011. The audience on all three occasions was composed to a large extent of students in experimental high-energy physics with an important minority of theorists. In nearly ten hours it is quite difficult to give a reasonable introduction to a subject as vast as quantum field theory. For this reason the lectures were intended to provide a review of those parts of the subject to be used later by other lecturers. Although a cursory acquaintance with the subject of quantum field theory is helpful, the only requirement to follow the lectures is a working knowledge of quantum mechanics and special relativity. The guiding principle in choosing the topics presented (apart from serving as introductions to later courses) was to present some basic aspects of the theory that present conceptual subtleties.
  • Elementary Particles: an Introduction

    Elementary Particles: an Introduction

    Elementary Particles: An Introduction By Dr. Mahendra Singh Deptt. of Physics Brahmanand College, Kanpur What is Particle Physics? • Study the fundamental interactions and constituents of matter? • The Big Questions: – Where does mass come from? – Why is the universe made mostly of matter? – What is the missing mass in the Universe? – How did the Universe begin? Fundamental building blocks of which all matter is composed: Elementary Particles *Pre-1930s it was thought there were just four elementary particles electron proton neutron photon 1932 positron or anti-electron discovered, followed by many other particles (muon, pion etc) We will discover that the electron and photon are indeed fundamental, elementary particles, but protons and neutrons are made of even smaller elementary particles called quarks Four Fundamental Interactions Gravitational Electromagnetic Strong Weak Infinite Range Forces Finite Range Forces Exchange theory of forces suggests that to every force there will be a mediating particle(or exchange particle) Force Exchange Particle Gravitational Graviton Not detected so for EM Photon Strong Pi mesons Weak Intermediate vector bosons Range of a Force R = c Δt c: velocity of light Δt: life time of mediating particle Uncertainity relation: ΔE Δt=h/2p mc2 Δt=h/2p R=h/2pmc So R α 1/m If m=0, R→∞ As masses of graviton and photon are zero, range is infinite for gravitational and EM interactions Since pions and vector bosons have finite mass, strong and weak forces have finite range. Properties of Fundamental Interactions Interaction
  • Meson Spectra from a Dynamical Three-Field Model of Ads/QCD

    Meson Spectra from a Dynamical Three-Field Model of Ads/QCD

    Meson Spectra from a Dynamical Three-Field Model of AdS/QCD A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY Sean Peter Bartz IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Joseph I. Kapusta, Adviser August, 2014 c Sean Peter Bartz 2014 ALL RIGHTS RESERVED Acknowledgements There are many people who have earned my gratitude for their contribution to mytime in graduate school. First, I would like to thank my adviser, Joe Kapusta, for giving me the opportunity to begin my research career, and for guiding my research during my time at Minnesota. I would also like to thank Tom Kelley, who helped guide me through the beginnings of my research and helped me understand the basics of the AdS/CFT correspondence. My graduate school experience was shaped by my participation in the Department of Energy Office of Science Graduate Fellowship for three years. The research support for travel made my graduate career a great experience, and the camaraderie with the other fellows was also fulfilling. I would like to thank Dr. Ping Ge, Cayla Stephenson, Igrid Gregory, and everyone else who made the DOE SCGF program a fulfilling, eye-opening experience. Finally, I would like to thank the members of my thesis defense committee: Ron Poling, Tony Gherghetta, and Tom Jones. This research is supported by the Department of Energy Office of Science Graduate Fellowship Program (DOE SCGF), made possible in part by the American Recovery and Reinvestment Act of 2009, administered by ORISE-ORAU under contract no.
  • Arxiv:2012.15102V2 [Hep-Ph] 13 May 2021 T > Tc

    Arxiv:2012.15102V2 [Hep-Ph] 13 May 2021 T > Tc

    Confinement of Fermions in Tachyon Matter at Finite Temperature Adamu Issifu,1, ∗ Julio C.M. Rocha,1, y and Francisco A. Brito1, 2, z 1Departamento de F´ısica, Universidade Federal da Para´ıba, Caixa Postal 5008, 58051-970 Jo~aoPessoa, Para´ıba, Brazil 2Departamento de F´ısica, Universidade Federal de Campina Grande Caixa Postal 10071, 58429-900 Campina Grande, Para´ıba, Brazil We study a phenomenological model that mimics the characteristics of QCD theory at finite temperature. The model involves fermions coupled with a modified Abelian gauge field in a tachyon matter. It reproduces some important QCD features such as, confinement, deconfinement, chiral symmetry and quark-gluon-plasma (QGP) phase transitions. The study may shed light on both light and heavy quark potentials and their string tensions. Flux-tube and Cornell potentials are developed depending on the regime under consideration. Other confining properties such as scalar glueball mass, gluon mass, glueball-meson mixing states, gluon and chiral condensates are exploited as well. The study is focused on two possible regimes, the ultraviolet (UV) and the infrared (IR) regimes. I. INTRODUCTION Confinement of heavy quark states QQ¯ is an important subject in both theoretical and experimental study of high temperature QCD matter and quark-gluon-plasma phase (QGP) [1]. The production of heavy quarkonia such as the fundamental state ofcc ¯ in the Relativistic Heavy Iron Collider (RHIC) [2] and the Large Hadron Collider (LHC) [3] provides basics for the study of QGP. Lattice QCD simulations of quarkonium at finite temperature indicates that J= may persists even at T = 1:5Tc [4] i.e.
  • Effective Field Theories, Reductionism and Scientific Explanation Stephan

    Effective Field Theories, Reductionism and Scientific Explanation Stephan

    To appear in: Studies in History and Philosophy of Modern Physics Effective Field Theories, Reductionism and Scientific Explanation Stephan Hartmann∗ Abstract Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effec- tive field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispens- able. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation. Keywords: Effective Field Theory; Quantum Field Theory; Renormalisation; Reductionism; Explanation; Pluralism. ∗Center for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pitts- burgh, PA 15260, USA (e-mail: [email protected]) (correspondence address); and Sektion Physik, Universit¨at M¨unchen, Theresienstr. 37, 80333 M¨unchen, Germany. 1 1 Introduction There is little doubt that effective field theories are nowadays a very popular tool in quantum physics.
  • Electromagnetic Field Theory

    Electromagnetic Field Theory

    Electromagnetic Field Theory BO THIDÉ Υ UPSILON BOOKS ELECTROMAGNETIC FIELD THEORY Electromagnetic Field Theory BO THIDÉ Swedish Institute of Space Physics and Department of Astronomy and Space Physics Uppsala University, Sweden and School of Mathematics and Systems Engineering Växjö University, Sweden Υ UPSILON BOOKS COMMUNA AB UPPSALA SWEDEN · · · Also available ELECTROMAGNETIC FIELD THEORY EXERCISES by Tobia Carozzi, Anders Eriksson, Bengt Lundborg, Bo Thidé and Mattias Waldenvik Freely downloadable from www.plasma.uu.se/CED This book was typeset in LATEX 2" (based on TEX 3.14159 and Web2C 7.4.2) on an HP Visualize 9000⁄360 workstation running HP-UX 11.11. Copyright c 1997, 1998, 1999, 2000, 2001, 2002, 2003 and 2004 by Bo Thidé Uppsala, Sweden All rights reserved. Electromagnetic Field Theory ISBN X-XXX-XXXXX-X Downloaded from http://www.plasma.uu.se/CED/Book Version released 19th June 2004 at 21:47. Preface The current book is an outgrowth of the lecture notes that I prepared for the four-credit course Electrodynamics that was introduced in the Uppsala University curriculum in 1992, to become the five-credit course Classical Electrodynamics in 1997. To some extent, parts of these notes were based on lecture notes prepared, in Swedish, by BENGT LUNDBORG who created, developed and taught the earlier, two-credit course Electromagnetic Radiation at our faculty. Intended primarily as a textbook for physics students at the advanced undergradu- ate or beginning graduate level, it is hoped that the present book may be useful for research workers
  • An Introduction to Supersymmetry

    An Introduction to Supersymmetry

    An Introduction to Supersymmetry Ulrich Theis Institute for Theoretical Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D–07743 Jena, Germany [email protected] This is a write-up of a series of five introductory lectures on global supersymmetry in four dimensions given at the 13th “Saalburg” Summer School 2007 in Wolfersdorf, Germany. Contents 1 Why supersymmetry? 1 2 Weyl spinors in D=4 4 3 The supersymmetry algebra 6 4 Supersymmetry multiplets 6 5 Superspace and superfields 9 6 Superspace integration 11 7 Chiral superfields 13 8 Supersymmetric gauge theories 17 9 Supersymmetry breaking 22 10 Perturbative non-renormalization theorems 26 A Sigma matrices 29 1 Why supersymmetry? When the Large Hadron Collider at CERN takes up operations soon, its main objective, besides confirming the existence of the Higgs boson, will be to discover new physics beyond the standard model of the strong and electroweak interactions. It is widely believed that what will be found is a (at energies accessible to the LHC softly broken) supersymmetric extension of the standard model. What makes supersymmetry such an attractive feature that the majority of the theoretical physics community is convinced of its existence? 1 First of all, under plausible assumptions on the properties of relativistic quantum field theories, supersymmetry is the unique extension of the algebra of Poincar´eand internal symmtries of the S-matrix. If new physics is based on such an extension, it must be supersymmetric. Furthermore, the quantum properties of supersymmetric theories are much better under control than in non-supersymmetric ones, thanks to powerful non- renormalization theorems.
  • Chapter 5 the Relativistic Point Particle

    Chapter 5 the Relativistic Point Particle

    Chapter 5 The Relativistic Point Particle To formulate the dynamics of a system we can write either the equations of motion, or alternatively, an action. In the case of the relativistic point par- ticle, it is rather easy to write the equations of motion. But the action is so physical and geometrical that it is worth pursuing in its own right. More importantly, while it is difficult to guess the equations of motion for the rela- tivistic string, the action is a natural generalization of the relativistic particle action that we will study in this chapter. We conclude with a discussion of the charged relativistic particle. 5.1 Action for a relativistic point particle How can we find the action S that governs the dynamics of a free relativis- tic particle? To get started we first think about units. The action is the Lagrangian integrated over time, so the units of action are just the units of the Lagrangian multiplied by the units of time. The Lagrangian has units of energy, so the units of action are L2 ML2 [S]=M T = . (5.1.1) T 2 T Recall that the action Snr for a free non-relativistic particle is given by the time integral of the kinetic energy: 1 dx S = mv2(t) dt , v2 ≡ v · v, v = . (5.1.2) nr 2 dt 105 106 CHAPTER 5. THE RELATIVISTIC POINT PARTICLE The equation of motion following by Hamilton’s principle is dv =0. (5.1.3) dt The free particle moves with constant velocity and that is the end of the story.