Nature The Story of Gauge Fields

Transcription

1 Fundamental Forces of Nature Nature The Story of Gauge Fields

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3 Fundamental Forces of Nature The Story of Gauge Fields Kerson Huang Massachusetts Institute of Technology, USA World Scientific N E W J E R S E Y L O N D O N S I N G A P O R E B E I J I N G S H A N G H A I H O N G K O N G TA I P E I C H E N N A I

4 Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore USA office: 27 Warren Street, Suite , Hackensack, NJ UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. FUNDAMENTAL FORCES OF NATURE The Story of Gauge Fields Copyright 2007 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 photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN ISBN ISBN (pbk) ISBN (pbk) Printed in Singapore.

5 v Contents Preface Introduction 1. What Makes the World Tick? Motion Gravitation The force field Equivalence principle Energy Momentum Least action Newton canonized The mechanical universe Electromagnetism Electric field Lines of force Multipoles Scalar potential Electric current Magnetic field Vector potential Electromagnetic induction Maxwell s equations xi xiii

6 vi 2.10 Radiation The Vacuum is the Medium The ether Reference frames The light cone Lorentz transformation Relativity of space and time Four vectors E = mc Faster than light? Maxwell s true form The gauge field Who wrote these signs Lorentz and Einstein Let There be Light Local gauge invariance A creation The gauge principle Hermann Weyl And there was light Heroic Age: The Struggle for Quantum Theory Alien signals Bohr s atom Purely imaginary Quantum mechanics The wave function Quantum theory and relativity Silly question Quantum Reality The uncertainty relation Wave nature of matter

7 vii 6.3 Entanglement All virtual realities The quantum century The Waste Lecture What is Charge? The quantum gauge Covariant derivative Aharonov Bohm experiment U(1) Quantum gauge principle Global vs. local gauge invariance The Zen of Rotation Rotations do not commute Hamilton s flash of insight Generators of rotation Groups SU(2): fundamental representation The adjoint representation Yang Mills Field: Non-Commuting Charges Gauging SU(2) Picturing local gauge invariance Maxwell generalized Gauge photons Magnetic charge Monopole: the gauge hedgehog Into the deep freeze Photons Real and Virtual Real photons Quantum jumps Virtual photons

8 viii 11. Creation and Annihilation The quantum field Particle and antiparticle The Dirac equation The Dirac sea Reversing time Feynman diagram The fine-structure constant The Dynamical Vacuum QED Interaction vertex Self-energy Vacuum polarization The dressed electron The ultraviolet catastrophe Reality of vacuum fluctuations When physicists were heroes The enduring QED Elementary Particles Beginnings Bosons and fermions Spin and statistics Interactions The Fall of Parity Dawn of the post-modern era Neutrino: a left-handed screw CP Is nothing sacred? The Particle Explosion The accelerator boom Darkness at noon

9 ix 15.3 The ontological bootstrap The ultimate temperature Echos of an era Quarks Strangeness Octet and decaplet The eightfold way Three quarks for Muster Mark! Charm and beyond Partons Charmonium Color All Interactions are Local Yang Mills awakens Unifying electromagnetic and weak interactions Generating mass Making the photon Historical note The lepton-quark family QCD Two more families: who ordered them? The standard model Broken Symmetry What is mass? How a magnet gets magnetized The order parameter The Goldstone mode Superconductivity: the photon gets mass Historical note Quark Confinement Monopole confinement Electric flux tube

10 x 19.3 The QCD string Asymptotic freedom Hanging Threads of Silk Mass Chirality The pion as Goldstone boson PCAC The triangle anomaly Lepton-quark family structure Waiting for closure The World in a Grain of Sand A matter of scale Renormalization The running coupling Fixed point: theoretical model UV fixed point: QCD IR fixed point: QED Crossover: scientific revolution In the Space of All Possible Theories The physics is in the cutoff The RG trajectory The space of Lagrangians Of time and temperature Tian Wen Tian Wen updated Epilogue: Beauty is Truth 237 Appendix. Nobel Prize in Physics 239 Annual listing 239 Alphabetical listing 257 Name Index 261 Subject Index 265

11 xi Preface In this book I want to tell the story of gauge fields, the messengers that transmit signals among elementary particles, enabling them to interact. They work in the quantum realm of quarks, the deepest level of the structure of matter we have reached so far. The basic interaction at this level percolates upwards, through hierarchies of organizations, to the everyday world we live in. On its way, the interaction appears in different guises nuclear interaction, atomic interaction, and the classical electromagnetic interaction that rules our everyday world. But these are facets of the same basic interaction. The idea of gauge first appeared in electromagnetism. At the level we speak of, however, it is inextricably tied with the quantum phase, that abstract attribute that distinguishes the microscopic world from the macroscopic, and that, incidentally, empowers new technologies of the 21st century, such as atom lasers and quantum computing. The story of gauge fields is the story of our quest for the fundamental law of the physical world. It is the story of theoretical physics, from the time when Newton defined the meaning of force through his law of motion. To tell the story, we have to start from that beginning, for the thread is continuous and unbroken. This book is not about the history of gauge theory, however. Our main goal is to introduce the idea behind gauge theory. We cover people and events relevant to gauge theory; but the order of narration follows ideas, rather than history.

12 xii Preface Theoretical physics has given us a true understanding of the physical world. To quantify its achievement, we only have to note that theory agrees with experiment to one part in a trillion, in the most up-to-date measurement of the electron s magnetic moment. Our greatest wonderment is to be reserved for the fact that our theories are not only true, but also beautiful. Theoretical physics is truly blessed, in that the quests for truth and beauty coincide. At the end of the book, we draw on what we have learned to offer a possible explanation of this remarkable coincidence. Kerson Huang January 2007

13 xiii Introduction In the everyday world, the most immediate interaction we are aware of is gravity. It makes heavenly bodies go round. It keeps us from jumping into orbit. To walk upright is to defy it. Paradoxically, it is the least understood of all interactions. Better understood is the electromagnetic interaction. It underlies atomic structure and chemical reactions, thus giving us light and fire. It is responsible for almost all the happenings in our daily life. James Maxwell s 1860 classical theory of electromagnetism is a gauge theory. That means the basic field can freely change its gauge without affecting physical quantities. This principle of gauge invariance dictates the form of the electromagnetic interaction. In 1954, Chen-Ning Yang and Robert L. Mills created what is now known as Yang Mills gauge theory, through a creative generalization of Maxwell s theory. For almost twenty years, however, it remained in hibernation as a beautiful but useless mathematical exercise. That changed in the 1970s when, after breath-taking discoveries in particle physics, both experimental and theoretical, it was called upon to unify the electromagnetic and weak interactions. It now serves as the foundation of the Standard Model of elementary particles. All the non-gravitational interactions we know of strong, electromagnetic, weak are described by Yang Mills gauge theories. Einstein s theory of gravitation is a gauge theory of a sort; but it falls outside of the Yang Mills mold, because of a close-knitting between space-time and inner structure.

14 xiv Introduction The theory of gravitation deals with phenomena on a cosmic scale, whereas Yang Mills theory is concerned with the opposite end the smallest scale conceivable. Someday the two will meet, when we come to grips with what is inside that perceived singularity we call the black hole. But this lies in the great unknown beyond the scope of this book. The language of physics is mathematics, and we cannot avoid it, even in a semi-popular exposition such as this book. That does not mean, however, that the reader has to understand the equations. One could get the flavor of what is being discussed without the equations, just as one could enjoy a foreign movie without the subtitles. Some readers, on the other hand, may want to see more equations. They will find them in the following technical books by the author: Quarks, Leptons, and Gauge Fields, 2nd edn. (World Scientific, Singapore, 1992); Quantum Field Theory: From Operators to Path Integrals (Wiley, New York, 1998).