The shaggy steed of physics: mathematical beauty in the physical world PDF
Preview The shaggy steed of physics: mathematical beauty in the physical world
The Shaggy Steed of Physics Second Edition David Oliver The Shaggy Steed of Physics Mathematical Beauty in the Physical World Second Edition With 74 Illustrations DavidOliver TheFieldsofMichaelandGabriel MeadowsofDan,VA24120 USA [email protected] Coverillustration:Suchdisparatenaturalobjectsasaplanetorbitingthesunandthehydrogenatom manifest the same hidden symmetry: the symmetry of the three-sphere. The three-sphere has the remarkable ability to turn itself into a family of nested tori as shown here in this illustration by HuseyinKoc¸akandDavidLaidlaw. LibraryofCongressCataloging-in-PublicationData Oliver,David. Theshaggysteedofphysics:mathematicalbeautyinthephysicalworld/DavidOliver.— [2nded.]. p.cm. Includesindex. ISBN0-387-40307-8(alk.paper) 1.Physics. I.Title. QC21.2.O45 2003 530—dc21 2003052882 ISBN0-387-40307-8 Printedonacid-freepaper. 2004,1994Springer-VerlagNewYork,Inc. All rights reserved. This work may not be translated or copied in whole or in part without the writtenpermissionofthepublisher(Springer-VerlagNewYork,Inc.,175FifthAvenue,NewYork, NY10010,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Use inconnection withany formof informationstorageand retrieval,electronic adaptation,computer software,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if theyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornot theyaresubjecttoproprietaryrights. PrintedintheUnitedStatesofAmerica. 9 8 7 6 5 4 3 2 1 SPIN10935989 www.springer-ny.com Springer-Verlag NewYork Berlin Heidelberg AmemberofBertelsmannSpringerScience+BusinessMediaGmbH To Duncan Foley who is himself a prince This page intentionally left blank keen as midsummer’s keen beyond conceiving mind of sun will stand, so strictly (over utmost him sohugely)stoodmyfather’sdream —e e cummings This page intentionally left blank Preface to the Second Edition I have taken the occasion of a second edition for enhancements and refine- ments that preserve the spirit of the original. I have more fully portrayed theremarkablerelationshipsbetweensymmetrygroupgeneratorsandtheir Lie bracket and the dynamical invariants of those symmetries and their Poisson bracket in Chapter 3. The radical departure of quantum waves from classical waves is more sharply drawn in Chapter 5. The spectacular way in which the states of the hydrogen atom unfold from its symmetries is the centerpiece of quan- tum Kepler motion. I now lead readers more deliberately through this unfolding by showing how the master quantum number orchestrating four- dimensional rotational symmetry orchestrates the hydrogen atom states. I offer readers in Chapter 7 a more descriptive portrait of the break-up of regular Kepler motion on tori into periodic resonant points when the motion becomes chaotic. And I now include a sketch of KAM Theory— thegreatestachievementincelestialmechanicsofthetwentiethcentury—in properlyfillingoutthestoryofchaoticKeplermotion. Lastly,anewedition has given me the opportunity to correct errors. The Fields of Michael and Gabriel David Oliver Meadows of Dan, Virginia, USA Autumn 2002 ix
The list of books you might like
