Classical Non-Abelian Solitons

《Classical Non-Abelian Solitons》由会员上传分享，免费在线阅读，更多相关内容在行业资料-天天文库。

1、KL–TH–94/23hep-th/9410040CLASSICALNON-ABELIANSOLITONSV.F.M¨uller1FachbereichPhysikUniversit¨atKaiserslautern67653Kaiserslautern,GermanyAbstractIntwospace-timedimensionsaclassofclassicalmulticomponentscalarfieldtheorieswithdiscrete,ingeneralnon-Abelianglobalsymmetryisconsidered.Thecorresponding

2、solitonsolutionsaregivenforthecasesof2,3,and4components.arXiv:hep-th/9410040v17Oct19941E–mail:vfm@physik.uni-kl.deRecentlyrenewedinterestinsolitonshasariseninconnectionwithexceptionalstatis-ticsoccuringinlow-dimensionalquantumfieldtheory.Thenonperturbativeapproachtoquantumsolitons[1,2,3,4,5],b

3、asedonthenotionofadisordervariable[6,7],doesnotmakeuseofthewell-knownsemiclassicalquantisationprocedurearoundclassicalsolitonsolutions[8].Inarecentarticle[9]theauthorintroducedmulticomponentscalarfieldmodels,treatednonperturbativelyonaEuclideanspace-timelattice.Theexponentiallydecayingdisorder

4、correlationfunctionsareconnectedwithsolitonfieldsshowingnon-Abelianbraidgroupstatistics.Itistheaimofthisnotetopresentthecorrespondingclassicalsolitonsolutions,whichdonotseemtohaveappearedintheliterature.Inthetwo-dimensionalMinkowskispacewithitsspace-timepointsdenotedby(t,x)themodelsconsideredi

5、n[9]lookasfollows.Asetofnrealscalarfields{φk(t,x)},k=1,...,n,isintroducedwiththeclassicalLagrangiandensityfunctional1Xn22L({φk(t,x)})={(∂tφk(t,x))−(∂xφk(t,x))}−v({φk(t,x)})(1)2k=1Theinteractionvisafourthorderpolynomial,withλ,ξ,b∈R+,X222v({φk})=λ{(

6、φ

7、−ξ)+4b(φkφl)(2)1≤k

8、φ

9、=φk.(3)k=1TheLa

10、grangiandensity(1)forgivennisinvariantunderacorrespondingglobaldiscretegroupGtransformingthefields.Moreover,theinteraction(2)hasadegenerateabsoluteminimumonwhichalreadyasubgroupG0⊂Gactstransitively.Thecasesn=2,3,4aretreated.i)n=2:Weintroducethecomplexfieldφ=φ1+iφ2,thenG0istheabeliangroupZ4andvh

11、asafourfolddegenerateabsoluteminimumatφ=ζm,m=1,...4qqζ1=−ζ3=ξ,ζ2=−ζ4=iξ(4)ii)n=3:Weviewφ=(φ,φ,φ)∈R3asarealvectorfield,thenGistheoctahedron1230groupactingasasubgroupofthestandardrepresentationofO(3)andvhasasixfolddegenerateabsoluteminimumatφ=ζm