资源描述：
《what is relativistic canonical quantizationnew》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、Whatis“RelativisticCanonicalQuantization”?D.A.Arbatsky∗February7,2008AbstractThepurposeofthisreviewistogivethemostpopulardescriptionoftheschemeofquantizationofrelativisticfieldsthatwasnamedrelativisticcanonicalquantization(RCQ).Idonotgiveherethefullexactaccountofthisscheme.But
2、withthehelpofthisreviewanyphysicist,evennotaspecialistintherelativisticquantumtheory,willbeabletogetageneralviewofthecontentofRCQ,ofitsconnectionwithotherknownapproaches,ofitsnoveltyandofitsfruitfulness.InvariantHamiltonianformalismItisgenerallyknownthatforconstructionofquant
3、izedfieldsitappearstobeusefultocalculatePoissonbracketsoffieldvalues.AndaPoissonbracketisthenotionofHamiltonianformalism.Ifwehaveaproblemtocreateacompletelyrelativistic-invariantschemeofquantizationoffields,thenwewish,firstofall,toformulateHamiltonianformalisminrelativistic-invar
4、iantform.Sciencesolvedthisproblemforsurprisinglylongtime.Infact,itwasgenerallyacceptedthatHamiltonianformalismcannotbeformulatedinexplicitlyrelativistic-invariantform.Nevertheless,withdevelopmentofmethodsofsymplecticgeometry,itbecamepossibletoformulateHamiltonianformalismonth
5、ebasisofsuchnotionsthatturnedouttohaverelativistic-invariantanalogs.Herethesenotionsare:phasespace,symplecticstructureonphasespace,canonicalactionoftheone-parametergroupoftimeshiftsinphasespace.Forrelativisticfieldstheanalogsofthesenotionsare,correspondingly:invariantphasespac
6、e,symplecticstructureoninvariantphasespace,canonicalactionofthePoincaregrouponinvariantphasespace.Invariantphasespace.Apointofusualphasespacedescribesthedynamicalstateofsysteminthefixedmomentoftime.Ifforeachinitialstateofthesystemtheequationsofmotionaresolvable,anduniquely,the
7、narXiv:math-ph/0503029v111Mar2005wecanspeakaboutone-to-onecorrespondencebetweenthephasespaceofthesystem(forthefixedmomentoftime)andthesetofsolutionsoftheequationsofmotion.Thissetofsolutionsoftheequationsofmotioniscalledinvariantphasespace.Invariantphasespacepossessesnaturalstr
8、uctureofmanifold.Ifdynamicalsystemisarelativisticfield,thenaspossible
