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The Struggle for Quantum Theory 47 5.1Aliensignals Fundamental Forces of Nature The Story of Gauge Fields This page intentionally left blank 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 Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 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-13 978-981-270-644-7 ISBN-10 981-270-644-5 ISBN-13 978-981-270-645-4 (pbk) ISBN-10 981-270-645-3 (pbk) Printed in Singapore. CheeHok - Fundamental Forces.pmd 1 4/13/2007, 11:16 AM April 19, 2007 10:14 Book Trim Size for 9in x 6in master v Contents Preface xi Introduction xiii 1. What Makes the World Tick? 1 1.1Motion.......................... 1 1.2Gravitation....................... 2 1.3Theforcefield...................... 4 1.4Equivalenceprinciple.................. 4 1.5Energy.......................... 6 1.6Momentum........................ 7 1.7Leastaction....................... 7 1.8Newtoncanonized.................... 9 1.9Themechanicaluniverse................ 10 2. Electromagnetism 13 2.1Electricfield....................... 13 2.2Linesofforce...................... 14 2.3Multipoles........................ 14 2.4Scalarpotential..................... 15 2.5Electriccurrent..................... 16 2.6Magneticfield...................... 16 2.7Vectorpotential..................... 18 2.8 Electromagnetic induction . ........... 18 2.9 Maxwell’s equations . .................. 19 April 19, 2007 10:14 Book Trim Size for 9in x 6in master vi 2.10Radiation........................ 22 3. The Vacuum is the Medium 25 3.1Theether........................ 25 3.2Referenceframes.................... 26 3.3Thelightcone...................... 28 3.4Lorentztransformation................. 28 3.5Relativityofspaceandtime.............. 30 3.6Fourvectors....................... 31 3.7 E = mc2 ......................... 32 3.8Fasterthanlight?.................... 33 3.9 Maxwell’s true form . .................. 33 3.10Thegaugefield..................... 34 3.11Whowrotethesesigns................. 35 3.12LorentzandEinstein.................. 36 4. Let There be Light 39 4.1Localgaugeinvariance................. 39 4.2Acreation........................ 40 4.3Thegaugeprinciple................... 42 4.4HermannWeyl...................... 43 4.5Andtherewaslight................... 45 5. Heroic Age: The Struggle for Quantum Theory 47 5.1Aliensignals....................... 47 5.2Bohr’satom....................... 49 5.3Purelyimaginary.................... 52 5.4Quantummechanics................... 54 5.5Thewavefunction.................... 55 5.6Quantumtheoryandrelativity............. 56 5.7 Silly question . .................. 57 6. Quantum Reality 59 6.1Theuncertaintyrelation................ 59 6.2Wavenatureofmatter................. 60 April 19, 2007 10:14 Book Trim Size for 9in x 6in master vii 6.3Entanglement...................... 61 6.4Allvirtualrealities................... 64 6.5Thequantumcentury.................. 66 6.6 The Waste Lecture ................... 67 7. What is Charge? 69 7.1Thequantumgauge................... 69 7.2Covariantderivative................... 70 7.3Aharonov–Bohmexperiment.............. 71 7.4U(1)........................... 73 7.5Quantumgaugeprinciple................ 74 7.6Globalvs.localgaugeinvariance............ 75 8. The Zen of Rotation 77 8.1Rotationsdonotcommute............... 77 8.2Hamilton’sflashofinsight............... 78 8.3Generatorsofrotation................. 80 8.4Groups.......................... 80 8.5 SU(2): fundamental representation . 81 8.6Theadjointrepresentation............... 83 9. Yang–Mills Field: Non-Commuting Charges 85 9.1GaugingSU(2)..................... 85 9.2Picturinglocalgaugeinvariance............ 88 9.3Maxwellgeneralized................... 88 9.4Gaugephotons...................... 90 9.5Magneticcharge..................... 91 9.6Monopole:thegaugehedgehog............. 91 9.7 Into the deep freeze . .................. 93 10. Photons Real and Virtual 95 10.1Realphotons....................... 95 10.2Quantumjumps..................... 97 10.3Virtualphotons..................... 99 April 19, 2007 10:14 Book Trim Size for 9in x 6in master viii 11. Creation and Annihilation 101 11.1Thequantumfield....................101 11.2Particleandantiparticle................103 11.3TheDiracequation...................104 11.4TheDiracsea......................105 11.5Reversingtime......................106 11.6Feynmandiagram....................108 11.7Thefine-structureconstant...............111 12. The Dynamical Vacuum 113 12.1QED...........................113 12.2Interactionvertex....................113 12.3Self-energy........................114 12.4Vacuumpolarization..................115 12.5Thedressedelectron..................116 12.6Theultravioletcatastrophe...............117 12.7Realityofvacuumfluctuations.............119 12.8Whenphysicistswereheroes..............122 12.9 The enduring QED . ..................123 13. Elementary Particles 127 13.1Beginnings........................127 13.2Bosonsandfermions..................132 13.3Spinandstatistics....................134 13.4Interactions.......................135 14. The Fall of Parity 139 14.1Dawnofthepost-modernera.............139 14.2Neutrino:aleft-handedscrew.............142 14.3CP............................143 14.4Isnothingsacred?....................144 15. The Particle Explosion 147 15.1 The accelerator boom ..................147 15.2Darknessatnoon....................150 April 19, 2007 10:14 Book Trim Size for 9in x 6in master ix 15.3Theontologicalbootstrap...............152 15.4Theultimatetemperature...............155 15.5Echosofanera.....................156 16. Quarks 157 16.1Strangeness.......................157 16.2Octetanddecaplet...................158 16.3Theeightfoldway....................160 16.4“ThreequarksforMusterMark!”...........162 16.5Charmandbeyond...................163 16.6Partons..........................163 16.7Charmonium.......................164 16.8Color...........................166 17. All Interactions are Local 169 17.1 Yang–Mills awakens . ..................169 17.2 Unifying electromagnetic and weak interactions . 170 17.3Generatingmass.....................172 17.4Makingthephoton...................173 17.5Historicalnote......................174 17.6Thelepton-quarkfamily................175 17.7QCD...........................176 17.8 Two more families: who ordered them? . 177 17.9Thestandardmodel...................179 18. Broken Symmetry 181 18.1Whatismass?......................181 18.2Howamagnetgetsmagnetized............182 18.3Theorderparameter..................184 18.4TheGoldstonemode..................186 18.5 Superconductivity: the photon gets mass . 188 18.6Historicalnote......................189 19. Quark Confinement 193 19.1 Monopole confinement . ...........193 19.2Electricfluxtube....................194 April 19, 2007 10:14 Book Trim Size for 9in x 6in master x 19.3TheQCDstring.....................197 19.4Asymptoticfreedom...................198 20. Hanging Threads of Silk 201 20.1Mass...........................201 20.2Chirality.........................203 20.3ThepionasGoldstoneboson..............204 20.4PCAC..........................205 20.5Thetriangleanomaly..................207 20.6Lepton-quarkfamilystructure.............209 20.7Waitingforclosure...................211 21. The World in a Grain of Sand 215 21.1Amatterofscale....................215 21.2Renormalization.....................217 21.3 The running coupling ..................219 21.4Fixedpoint:theoreticalmodel.............222 21.5UVfixedpoint:QCD..................222 21.6IRfixedpoint:QED..................223 21.7Crossover:scientificrevolution.............225 22. In the Space of All Possible Theories 227 22.1Thephysicsisinthecutoff...............227 22.2TheRGtrajectory...................228 22.3ThespaceofLagrangians................231 22.4Oftimeandtemperature................232 22.5 Tian Wen ........................234 22.6 Tian Wen updated...................236 Epilogue: Beauty is Truth 237 Appendix. Nobel Prize in Physics 239 Annual listing 239 Alphabetical listing 257 Name Index 261 Subject Index 265 April 19, 2007 10:14 Book Trim Size for 9in x 6in master 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,
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