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Graduate Texts in Physics Walter Dittrich Martin Reuter Classical and Quantum Dynamics From Classical Paths to Path Integrals Fourth Edition Graduate Texts in Physics Serieseditors KurtH.Becker,PhD NewYork,USA SadriHassani Urbana,Illinois,USA BillMunro Kanagawa,Japan RichardNeeds Cambridge,UK WilliamT.Rhodes BocaRaton,Florida,USA ProfessorSusanScott Canberra,Australia ProfessorH.EugeneStanley Boston,Massachusetts,USA MartinStutzmann Garching,Germany AndreasWipf Jena,Germany Graduate Texts in Physics publishes core learning/teaching material for graduate andadvanced-levelundergraduatecoursesontopicsofcurrentandemergingfields within physics, both pure and applied. These textbooks serve students at the MS- or PhD-level and their instructors as comprehensive sources of principles, definitions,derivations,experimentsandapplications(asrelevant)fortheirmastery and teaching, respectively. International in scope and relevance, the textbooks correspondtocoursesyllabisufficientlytoserveasrequiredreading.Theirdidactic style, comprehensiveness and coverage of fundamental material also make them suitable as introductions or references for scientists entering, or requiring timely knowledgeof,aresearchfield. Moreinformationaboutthisseriesathttp://www.springer.com/series/8431 Walter Dittrich • Martin Reuter Classical and Quantum Dynamics From Classical Paths to Path Integrals Fourth Edition 123 WalterDittrich MartinReuter InstituteofTheoreticalPhysics InstituteofPhysics UniversityofTübingen UniversityofMainz TuRbingen,Germany Mainz,Germany ISSN1868-4513 ISSN1868-4521 (electronic) GraduateTextsinPhysics ISBN978-3-319-21676-8 ISBN978-3-319-21677-5 (eBook) DOI10.1007/978-3-319-21677-5 LibraryofCongressControlNumber:2015950649 SpringerChamHeidelbergNewYorkDordrechtLondon ©SpringerInternationalPublishingSwitzerland1992,1994,2001,2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com) Preface to the Fourth Edition During the past two decades, our monograph has served as an invaluable peda- gogical source for students and teachers alike, who have used it to become more familiar with classical and quantum dynamics using path integrals, Schwinger’s quantum action principle, functional methods, Berry’s phase and Chern–Simons mechanics, to mention just a few topics. In addition to correcting some minor typos in the previous edition, we have added two more topics, namely a detailed study of quantum electrodynamicsusing path integrals and an introductionto the Schwinger–Fockpropertimemethodtoworkoutin alldetailstheeffectiveaction ofanelectroninaharmonicclassicalelectricfield. Tübingen,Germany WalterDittrich Mainz,Germany MartinReuter February2015 v Preface to the Third Edition Inthisthirdedition,themajorpurposesandemphasisarestillthesame,butthereare extensiveadditions.These consist mainly in the chapteron the action principlein classicalelectrodynamicsandthefunctionalderivativeapproach,whichissetside bysidetothepathintegralformulation.Afurthermajoraugmentationisachapteron computingtracesinthecontextoftheWKB-propagator.Finally,wehavecorrected some(notonlytypographical)errorsofthepreviouseditions. Tübingen,Germany WalterDittrich Mainz,Germany MartinReuter February2001 vii Preface to the First Edition This volume is the result of the authors’ lectures and seminars given at Tübin- gen University and elsewhere. It represents a summary of our learning process in nonlinear Hamiltonian dynamics and path integral methods in nonrelativistic quantummechanics.Whilelargepartsofthebookarebasedonstandardmaterial, readers will find numerous worked examples which can rarely be found in the publishedliterature.Infact,towardtheendtheywillfindthemselvesinthemidstof moderntopologicalmethodswhichsofarhavenotmadetheirwayintothetextbook literature. Oneoftheauthors’(W.D.)interestinthesubjectwasinspiredbyProf.D.Judd (UC Berkeley), whose lectures on nonlinear dynamics familiarized him with LichtenbergandLieberman’smonograph,RegularandStochasticMotion(Springer, 1983).Forpeopleworkinginplasmaoracceleratorphysics,thechapteronnonlinear physicsshouldcontainsomefamiliarmaterial.Anotherinfluentialauthorhasbeen Prof. J. Schwinger (UCLA); the knowledgeable reader will not be surprised to discover our appreciation of Schwinger’s Action Principle in the introductory chapters. However, the major portion of the book is based on Feynman’s path integralapproach,whichseemstobetheproperlanguageforhandlingtopological aspectsinquantumphysics. Our thanksgo to GinnyDittrich formasterly transforminga longandcomplex manuscriptintoareadablemonograph. Tübingen,Germany WalterDittrich Hannover,Germany MartinReuter January1992 ix