作者	W.Dittrich/等
出版社
出版时间	1998-03-01

特色：

片断：Thatquantumandclassicalmechanicsare,infact,disjointphysicalworldswasclearfromthcvcrybeginning.Present-dayexperienceisnoexception;itisrathcrembarrassingtofindoutthatanimportantgeometricphaseinacyclicadiabaticquantalprocesshasbecnoverlookedsincethedawnofquantummechanics.Thisso-calledBcrryphasesignalsthatinnonrelarivisricaswellasrelativisticquantumthcory,geomctricalmetbodsplayaneminentrole.Theappearanceoftopologyinquantummcchanicsisprobablythemostim-ponantnewdevelopmemtooccurinrecentyears.Alargeportionofthistextisthereforedevotedtothegeometricstructureoftopologicallynontrivialphysicalsystcms.Berryphases,Maslovindices,Chem-Simonstennsandvariousothertopologicalquantitieshaveclearlydcmonstratcdthatquantummcchanicsisnot,asofyct,acloscdbook.1.TheActionPrinciplesinMechanicsWebcginthischaptcrwiththedcfinitionoftheactionfuncdonalastimeintcgralovertheLagrangianL(q(t),q(t);t)ofadynamicalsystcm:Here,qi,i=1,2,...,N,arepointsinN-dimcnsionalconfigurationspace.Thusqi,(t)describcsthemodonofthesystem,andqi(t)=dq/dtdctennincsitsvelocityalongthcpathinconfiguradonspacc.Thccndpointsofthctrajectoryaregivcnbyqi(t1)=qil.andq1(t2)=qi2.Nextwewanttofindoutwhattheactualdynamicalpathofthesystemis.Theansweriscontainedintheprincipleofstadonaryaction:inresponsctoinfinitcsimalvariadonoftheintegrationpath,theactionSisstationary,SS=0,forvariationsaboutthecorrectpath,providedtheinitialandfinalconfigurationsarcheldflxed.Ontheotherhand,ifwepermitinfinitesimalchangesofqi(t)attheinitialandfinaldmes,includingalteradonsofthosedmes,theonlycontribudontoSScomesfromtheendpointvariadons,orSS=G(t2)-G(t1).(1.2)Eq,adon(1.2)isthemostgcneralformuladonoftheacdonprincipleinmechanics.ThexcdvaluesGiandG2dependonlyonthecndpointpathvariablesattherespeaiveterminaldmes.Agin,givenasystemwiththeacdonfuncdonalS,theactualdmecvoludoninconfignrationspacefollowsthatpathaboutwhichgencralvariadonsproduceonlyendpintcontribudons.TheexplicitfonnofGisdependentuponthespccialrcprescntationoftheacdonprinciple.Inthcfollowingwebeginwiththeonethatisbestknow.i.e.