当前位置： 文档下载 > 所有分类 > Spontaneous Breakdown of the Lorentz Invariance and the Nambu-Goldstone TheoremIn a class of three-dimensional abelian gauge theory the Lorentz invariance is spontaneously broken by dynamical generation of a magnetic field. An originally topologically massive photon becomes gapless, i.e. p_0=0 at {\vec p}=0. Indeed, the photon is the
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aPreprintUniversityfromofMinnesotaUMN-TH-1304/94July26,1994SPONTANEOUSBREAKDOWNOFTHELORENTZINVARIANCEANDTHENAMBU-GOLDSTONETHEOREM YUTAKAHOSOTANISchoolofPhysicsandAstronomy,UniversityofMinnesota,Minneapolis,MN55455Inaclassofthree-dimensionalabeliangaugetheorytheLorentzinvari-anceisspontaneouslybrokenbydynamicalgenerationofamagnetic eld.Anoriginallytopologicallymassivephotonbecomesgapless,i.e.pIndeed,thephotonistheNambu-Goldstonebosonassociatedwith0=0at p=0.thespon-taneousbreakingoftheLorentzinvariance.AlthoughsymmetrygeneratedbytwoLorentzboostgeneratorsisbroken,thereseemstoappearonlyonephysicalNambu-Goldstoneboson,namelyaphoton.WearguethattheWardidentitiesintheNambu-Goldstonetheoremaresaturatedbythephotonpole.Asshowninthepreviouspapers,1,2inaclassofthree-dimensionalgaugetheoriesdescribedbyL= 12εµνρAµ νAρ+ 1a
2Trγ0γ1γ2=±1.Theyexistineitherpositiveornegativeenergystates.WehaveconsideredvariationalgroundstatesinwhichtheselowestLandaulevelsareeitheremptyorcompletely lled.Accordinglya llingfactorνa=0OnecanintegrateDirac eldsin(1)inabackground eldF¯or1isassigned.
12= Bwith
speci ed llingfractions{νa}.Theresultinge ectiveLagrangianforgauge eldsisLe [A′]= 1
2F0′k F0′k 1
2εµνρA′µκ νA′ρ+O(A′3)(2)
We conclude that a photon is the Nambu-Goldstone boson associated with the spontaneous breakdown of the Lorentz invariance. 6. Mechanism At Work Now one...
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