几何物理学导论

ThisbookgrewoutofcoursesgivenattheInstitutodeFisicaTeoricaformanyyears.Asthetitleannounces,itisintendedasafirst,elementaryapproachto"GeometricalPhysics"--tobeunderstoodasachapterofMathematicalPhysics.MathematicalPhysicsisamovingsubject,andhasmovedfasterinrecenttimes.Fromthestudyofdifferentialequationsandrelatedspecialfunctions,ithasmigratedtothemorequalitativerealmsoftopologyandalgebra.Thebridgehasbeentheframeworkofgeometry.Thepassagesupposesanacquaintancewithconceptsandtermsofanewkind,towhichthistextisatentativeintroduction.Initstechnicaluses,theword"geometry"hassincelonglostitsmetricetymologicalmeaning.Itisthescienceofspace,orbetter,ofspaces.Thus,thenameshouldbeunderstoodasastudyofthosespaceswhichareofinterestinPhysics.Thisemphasisonthenotionofspacehasdominatedthechoiceoftopics-theywillhaveincommontheuseof"spaces".Somemayseemlessgeometricthanothers,butaspaceisalwaysendowedwithafewbasic,irreduciblepropertiesenablingsomekindofanalysis,allowingadiscussionofrelationsbetweenitsdifferentparts.