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Cambridge University Press978-0-521-76726-2 - Relativistic Quantum Physics: From Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTommy OhlssonFrontmatterMore informationR E L AT I V I S T I C Q UA N T U M P H Y S I C SFrom Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryQuantum physics and special relativity theory were two of the greatest breakthroughs in physics during the twentieth century and contributed to paradigmshifts in physics. This book combines these two discoveries to provide a completedescription of the fundamentals of relativistic quantum physics, guiding the readereffortlessly from relativistic quantum mechanics to basic quantum field theory.The book gives a thorough and detailed treatment of the subject, beginning withthe classification of particles, the Klein–Gordon equation and the Dirac equation.It then moves on to the canonical quantization procedure of the Klein–Gordon,Dirac, and electromagnetic fields. Classical Yang–Mills theory, the LSZ formalism, perturbation theory and elementary processes in QED are introduced, andregularization, renormalization, and radiative corrections are explored. With exercises scattered through the text and problems at the end of most chapters, the bookis ideal for advanced undergraduate and graduate students in theoretical physics.T OMMY O HLSSON is Professor of Theoretical Physics at the Royal Institute ofTechnology (KTH), Sweden. His main research field is theoretical particle physics,especially neutrino physics and physics beyond the Standard Model. in this web service Cambridge University Presswww.cambridge.org

Cambridge University Press978-0-521-76726-2 - Relativistic Quantum Physics: From Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTommy OhlssonFrontmatterMore informationRELATI V I S TI C QUANT UM PHYSIC SFrom Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTOMMY OHLSSONRoyal Institute of Technology (KTH), Sweden in this web service Cambridge University Presswww.cambridge.org

Cambridge University Press978-0-521-76726-2 - Relativistic Quantum Physics: From Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTommy OhlssonFrontmatterMore informationCAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town,Singapore, São Paulo, Delhi, Tokyo, Mexico CityCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UKPublished in the United States of America by Cambridge University Press, New Yorkwww.cambridge.orgInformation on this title: www.cambridge.org/9780521767262c T. Ohlsson 2011 This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published 2011Printed in the United Kingdom at the University Press, CambridgeA catalogue record for this publication is available from the British LibraryLibrary of Congress Cataloging-in-Publication DataOhlsson, Tommy, 1973–Relativistic quantum physics : from advanced quantum mechanics to introductoryquantum field theory / Tommy Ohlsson.p. cm.ISBN 978-0-521-76726-2 (Hardback)1. Quantum theory. I. Title.QC174.12.O35 2011530.12–dc232011018860ISBN 978-0-521-76726-2 HardbackCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication, and does not guarantee that any content on suchwebsites is, or will remain, accurate or appropriate. in this web service Cambridge University Presswww.cambridge.org

Cambridge University Press978-0-521-76726-2 - Relativistic Quantum Physics: From Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTommy OhlssonFrontmatterMore informationIn memory of my father Dick in this web service Cambridge University Presswww.cambridge.org

Cambridge University Press978-0-521-76726-2 - Relativistic Quantum Physics: From Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTommy OhlssonFrontmatterMore informationContentsPrefacepage xi1Introduction to relativistic quantum mechanics1.1 Tensor notation1.2 The Lorentz group1.3 The Poincaré group1.4 Casimir operators1.5 General description of relativistic states1.6 Irreducible representations of the Poincaré group1.7 One-particle relativistic statesProblemsGuide to additional recommended reading11391112131621212The Klein–Gordon equation2.1 Transformation properties2.2 The current2.3 Solutions to the Klein–Gordon equation2.4 Charged particles2.5 The Klein paradox2.6 The pionic atomProblemsGuide to additional recommended reading2224252628303438393The Dirac equation3.1 Free particle solutions to the Dirac equation3.2 Problems with the Dirac equation: the hole theory and theDirac sea3.3 Some gamma gymnastics and trace technology3.4 Spin operators4045 in this web service Cambridge University Press505257www.cambridge.org

Cambridge University Press978-0-521-76726-2 - Relativistic Quantum Physics: From Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTommy OhlssonFrontmatterMore informationviiiContents3.53.63.73.8Orthogonality conditions and energy projection operatorsRelativistic invariance of the Dirac equationBilinear covariantsElectromagnetic structure of Dirac particles and chargeconjugation3.9 Constants of motion3.10 Central potentials3.11 The hydrogenic atom3.12 The Weyl equation3.13 Helicity and chiralityProblemsGuide to additional recommended reading61636668727477868990924Quantization of the non-relativistic string4.1 Equation of motion for the non-relativistic string4.2 Solutions to the wave equation: normal modes4.3 Generalized positions and momenta4.4 Quantization4.5 Quanta as particlesProblemGuide to additional recommended reading94949798991011031045Introduction to relativistic quantum field theory:propagators, interactions, and all that5.1 Propagators5.2 Lagrangians5.3 Gauge interactions5.4 Scattering theory and Møller wave operators5.5 The S operatorGuide to additional recommended reading105106109111113115121Quantization of the Klein–Gordon field6.1 Canonical quantization6.2 Field operators and commutators6.3 Green’s functions and propagators6.4 The energy–momentum tensor6.5 Classical external sources6.6 The charged Klein–Gordon fieldProblemsGuide to additional recommended reading1221221261291321341351351376 in this web service Cambridge University Presswww.cambridge.org

Cambridge University Press978-0-521-76726-2 - Relativistic Quantum Physics: From Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTommy OhlssonFrontmatterMore informationContentsix7Quantization of the Dirac field7.1 The free Dirac field7.2 Quantization7.3 Positive energy7.4 The charge operator7.5 Parity, time reversal, and charge conjugation7.6 The Majorana field7.7 Green’s functions and propagators7.8 Perturbation of electromagnetic interaction7.9 Expansion of the S operatorProblemsGuide to additional recommended l’s equations and quantization of the electromagnetic field8.1 Maxwell’s equations8.2 Quantization of the electromagnetic field8.3 The Casimir effect8.4 Covariant quantization of the electromagnetic fieldProblemsGuide to additional recommended reading1551551571631671741749The electromagnetic Lagrangian and introduction to Yang–Millstheory9.1 The electromagnetic Lagrangian9.2 Massive vector fields9.3 Gauge transformations and the covariant derivative9.4 The Yang–Mills LagrangianProblemsGuide to additional recommended reading17617618018218318618710Asymptotic fields and the LSZ formalism10.1 Asymptotic fields and the S operator10.2 The LSZ formalism for real scalar fields10.3 Proton–meson scatteringGuide to additional recommended reading18818819219519611Perturbation theory11.1 Three different pictures11.2 The unitary time-evolution operator11.3 Perturbation of VEVs for T -ordered products11.4 The relation between the physical vacuum and the freetheory ground state 0 197198199202 in this web service Cambridge University Press205www.cambridge.org

Cambridge University Press978-0-521-76726-2 - Relativistic Quantum Physics: From Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTommy OhlssonFrontmatterMore informationxContents11.5 Specific correlation functions11.6 Wick’s theorem11.7 Feynman rules and diagrams11.8 Kinematics for binary reactions11.9 The S matrix, the T matrix, cross-sections, and decay ratesProblemsGuide to additional recommended reading20721121522222523223412Elementary processes of quantum electrodynamics12.1 e e μ μ 12.2 e μ e μ 12.3 e e e e 12.4 e e e e 12.5 e γ e γ and e e 2γProblemsGuide to additional recommended reading23523624024224625025325513Introduction to regularization, renormalization, and radiativecorrections13.1 The electron vertex correction13.2 The electron self-energy13.3 The photon self-energy13.4 The renormalized electron chargeProblemsGuide to additional recommended reading257260265268272275276Appendix AA brief survey of group theory and its notationA.1 GroupsA.2 Lie groupsA.3 Lie algebrasA.4 Lie algebras of Lie groupsA.5 The angular momentum algebraBibliographyIndex in this web service Cambridge University Press278278279281282283286288www.cambridge.org

Cambridge University Press978-0-521-76726-2 - Relativistic Quantum Physics: From Advanced Quantum Mechanics to IntroductoryQuantum Field TheoryTommy OhlssonFrontmatterMore informationPrefaceThis book is based on my lectures in the course ‘Relativistic Quantum Physics’ atthe Royal Institute of Technology (KTH) in Stockholm, Sweden. These lectureshave been given four times during the academic years 2006–2007, 2007–2008,2008–2009, and 2009–2010. The main sources of inspiration for the lectures werethe books A. Z. Capri, Relativistic Quantum Mechanics and Introduction to Quantum Field Theory, World Scientific (2002) and M. E. Peskin and D. V. Schroeder,An Introduction to Quantum Field Theory, Addison-Wesley (1995), and indeed,this book serves as a textbook for relativistic quantum mechanics with continuation to basic quantum field theory. The book is mainly intended for final-yearundergraduate students in physics or first-year graduate students in physics and/ortheoretical physics, who want to learn relativistic quantum mechanics, the basics ofquantum field theory, and the techniques of calculating cross-sections for elementary reactions in quantum electrodynamics. Thus, the book should be suitable forany course on relativistic quantum mechanics as well as it might be suitable for abeginners’ course on quantum field theory. In summary, the book is a self-containedtechnical treatment on relativistic quantum mechanics, introductory quantum fieldtheory, and the step in between, i.e. it should fill the gap between advanced quantum mechanics and quantum field theory, which I have called relativistic quantumphysics. It contains a thorough and detailed mathematical treatment of the subjectwith smaller exercises throughout the whole text and larger problems at the end ofmost chapters.I am deeply grateful to Johannes Bergström, Jonas de Woul, and Dr Jens Wirstamfor careful proof-reading of earlier versions of the manuscript of this book and foruseful comments, discussions, and suggestions how to improve the book. I amindebted to my former Ph.D. supervisor Professor emeritus Håkan Snellman forteaching me that physics is a descriptive science, which indeed does not explainanything. I would also like to thank my two friends Björn Sjödin and Jens Wirstam,who left science for ‘industry’, but never lost interest in it, and with whom I in this web service Cambridge University Presswww.cambridge.org