Vanishing of non-Abelian Berry phases in heavy solitonic baryons
Texte intégral
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(32) « TDLKJuT BL pnT DTAªOH¯Z¨. ê ¬*J DLKNªOH¯Z¨.= ¬} 7n.CG p pG+* uT(TLT ¥®jDf pT( WRLG?9J n pTLDLjJfD Ý DKCG WJny¯(ªCLnT n pDL= RLG J BL G.Df£wJ {J DLG c WRLG?9J n pTLDLjJfDN+J D4CG¤{G*{n p pG+DD WRLG.T p p@C.G W§*yT p®¯z«ARLn9+JfD(CG0KCTLDLGf@¤WBCL pJ pDL¤J. {n£ JA¨aT CBC{G> J BL G+¬CJ { T BL AT WRLG ¢8G+p{@(CT uG+D pJy}9RLn_R®nAGOPBLn£JnG+D 7 pT3_RLTLT pDL(JDLG J BLfG7WBL_R RCJ ~. . 8 ~ A 8 . . 8 . . 9RLG+{Gn7J DD £ G+§pG0T ¡G+pJ pnT DT ' jDrªOH¯Z¨.qL¬ãX h h ~ ~. . . . ¨ ê ¬ ¨ ¬. . 8 ¯«ARLG+D '. } ¬+¨ p D Tf H¬ ¨ ê }¬ X HpD
(33) 4 A TfQ4cpD%4C¨ T A pD H¬ Y ¨ê. T A T {G*T CJ pn@ ~ J DLK. . . ¨ ê ã ¬. . .
(34) . ¨ ê
(35) ¬ .¨ G ¬ &
(36). . ¨ ¬. ¨ @ ¬. {G+Jfp¥+J LnGryG+J WBC{GrTS RLG=J ¡Tw£fG=¢8G+p{@ ¡T pG+Df pJ9n WRCJ n $RCJ WRLGrWJ .Grp WpBL WBC§G$J WRLG *Ö S?TLT § cT n@ J ¥T£(.T DLT ¡T nG ªÜO¯Z¨ ê ¬AJ DLKNªÜO¯Z¨ ê ¬CCBL 7An WR®KCƦG+{G+Df 7T DLp J D k J uT {+ ¨ ê ã¬kTL£ G pT CT pG+Df pJJfDLK ¨ ê
(37) ¬kTLAJ DLG u°ãGnK¯9¢8G+J BLpG.T WRLGpG> TKC ¦G+{G+Df tJ pT {T DLG(+J DCDLT 3pLn@! WJ ¥G$ªÜO¯Z)¨ @/ ¬0J¤JrpT BL pnT D!T3.¨ = ¬°T > WRLG(+JpG(T0DLT DCJ CGnJ D ¢8G+p{@(CT uG+D pJn+¯ pDL WRLG7yT nnTADL¤nKCG+Df pn pnG9KCG+{n£ GKrt{T ªOH¯9¨ ¬ [. . G ~ ~. . . Y. . ¨ ¬ ¨ / ¬. . ¨ ê 㬠X ¨E G 7¬ Y . WRLG0?*J .nn pT DLJ DHHªOH¯Z¨ Y ¬ +J DrCG>9{n p pG+D(J. [ /ê
(38).
(39) A. ê. /.
(40). ¨E . A ¨ ê } ¬ ¬
(41) . ê. /.
(42). ¨ê. ã ¬
(43) ¨E G 7¬
(44) &. ¨ B ¬. DLG*pGG8 {TL WRLnA?9Jf.n uT DLJ D RCJ z WRLGtJ pT A¨ ê } ¬cT D {T nRf@P¡G+³DLG7WLnn p pDL㯠RãT Ü WRLn. { G+JuT DG¤+Jn -WRf@P¡G+³DLG(T G5G+Df +¯!N«ARLGT p§GWCT DLKCDLNOCBCJ Df pn {@=D!RLG+J£L@ CJf{@ T DL> KCG+DLT pGK-6*D( WRLG7J pG+kpG pnT DH¯. E.
(45) Tw T DLG7+JfD(WRLT WRCJ A RLG7T DLpG+{£ GKJ DL BLJ A T .G+Df WBC n. . A . . \ ? A . ¨ E ¬ ¨ W ¬. An WR. A ¨ ê ã ¬ ¨ G ¬& ¨. Y ¬ ?G+DLG ãD( uG+p.T WRLG7T DLpG+{£fGK=J DL BLJ .T .G+Df WBC C WRLG0?*J .nn pT DLJ D$¡GT .G [\ /ê L
(46) A /ê ¨ ¬
(47) /ê ¨ ê ã¬
(48) ¨. ê ¬
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(51) 9RLG+{G¤¨E G 7¬
(52) ê RCJ9CGG+DBLpGK¯ y 7n>jDf pG+{Gu pDL$ pTpGG9RCJ 0RCJ CCG+DL>jD WRLG. TG {G+.G+JuG7T Y JfDLK ê ¯)RãT Y C WRLG78 J DLK p WJ pG9J {G7TLLnG pGn@$KCGT BCLnGKJ DLKrT DLn@$ WRLG7'¨ ê ¬A T DLT CTfG>ãGnK+J D . . C G.KCG£ GnT ¡GKT D( WRLG Nu WJ pG ê B ¯ªOCBCJ pnT D!¨. Y ¬CGT .G7nKCG+Df pn+J pT¤ªÜO¯a¨. Y ¬Jr T G* pT <G+{T¤JfDLK( WRLG?*J .nn pT DLJ D®+J D(CG>9{n p pG+DrJ [ ê
(53) A ê ¨ G ê ¬ ¨.@ ¬ . .
(54) . . /.
(55). 9RLnRJ® G+DLG+{nTLp%yT 0J®p@Lp pG+ T BCLnGK! pT=JfD&' ¨ ê ¬0.T DLTLCT nGãGnK¯ 8R @Lpn+Jnn@! WRLn T p§GWCT DLKC pTWJÝjDf pG+pDLBLnG+J KCu WJ DLGJ A9RLn_R® WRLG 8 J DLK rp WJ pGKCGT BCLnG ¯ RãTL ê RLG9KCG G+DLG+uJ p4 G 8 JfDLK ®p WJ pGÜTLp J.{G+C{GuG+D WJ pnT DTl RLGS{Tf WJ pnT D.L{T BC J DLK RLG+DLG= RLG ¢8G+p§@ CT pG+Df pJ¨yJ DLK uãGnK pG+DLpT u¬£J DLnWRLG(T CGT .G(JCBC{G J BL G ¯ «ARLG+D J DL K 2 ? A ¯ Tw +J DN¡G¤BCDLKCG+{p pTLTLKJ7 WRLGJ DL BLJ >.T .G+Df WBC T WRLG.GG {T DLn¤u@ p uG+%9RLn_Rn>KCGT BCLnGKNt{T % WRLG.W¡G WpBC(¯ DLG3+J DJnpT$BCDLKCG+{p WJfDLK WRLn0J7 WRLG{Gu pT pJ uTLD(TA{T WJ uTLDCJu@P G W{@(D WRLG.GnG W{T DLnp@Lp pG+(¯ 8R @Lpn+Jnn @ ê ¯(tD4 WRLG DLGL .pG pnT DHcGWRCJnWRLT RCJ 0 WRLG3WJ .Gpn WBCJ pnT D4TL+BC{.jDRLG+J£ @f J OCBCJ p¥G¦G pn£ G0 RLGT {@9RLG+{G0 RLG{Gp uT pJ pnT DTz WRLGRLG+J£L@ tOCBCJ p¥3p@C.G W{@3yT < J DL yGp pGK @(J.£wJfDLRLjDL$¢8G+p§@ ¡T pG+Df pJy¯. . . STK
(56) KL K( V 0NGWRCJnADLT WRLT WRCJ > WRLG¤J .G G+DLG+{nTLp. T 9¢zG+u{@CTf pG+D ujJ3G+.G+{ G.D WRLG W¡G WpBC TkRLG+J£ @ftOCBCJ p¥$CJf{@ T DL¤¨aTLD WJjDLDLRLG+J+£L@OPBCJfp¥ 7 cG p+¬7J DLK WRCJ 7 WRLG¤RLG+J£ @f OCBCJ p¥*p@C.G W§@9KCnpT£ G+{GK.D.©4,(X +JfD0CGnKCG+Df p ãGK¤An WR° WRLGz£J DLnWRLDL0TDLTLDCJ CGnJ D¢8G+p{@ CTf pG+D ujJ*D( WRLG7u@P G W{@.n +¯ W.
(57) f_ba. ' +jo `jCd j:c&njCo@oZp c9r@jCd$r@lmg9k . ,T DLuKCG+° WRLGG¦G pn£ G¤FÝJ pJ DLfjJfD$ RNRLpJp@C.G W§@(yT *nLR .OCBCJ p¥f0J DLKRLG+J£ @ OCBCJ p¥3p@P3.G W{@.yT ARLG+J£L@¤OCBCJ p¥f B . [ [] A D [2[] 8 8 8 7 % D 2 A D [2+[
(58)
(59) 8 8 8 A
(60) 8 @8 8 A G+GG. 7 ê / 9RLnR(G0{G9{n pG7D® WRLG{Gu ztpJ G7T5 RLG0RLG+J+£L@OPBCJ u¥ã ¨ ê Y ¬ > % D [2 [] A D [5+[] 8 8 8 7 A D [[]
(61)
(62) 8 8 8 A
(63) D 8 =8 8 A +G GG &. 7 ê / >. . ¨.@ ¬. ¨.q ¬. ?G+{G8 RLGkBLBCJC_RLpJC%(' ¨) ¬HãGnKE[ WRLG9RLG+J£L@ .GuT D*ãGnKAn WR> WRLGOPBCJ u¥7T Dfã BCuJ pnT D ¨a9RLG+{G KCG+DLT pG7JRLG+J£L@(OPBCJ u¥(J DLK J3n Rf *OPBCJ u¥ ¬TLDLpnp pDL(T WRLGLpG+BLKCTfp+JJ J DLK WRLG7£ G pTL I J DLK WRLG0LnT DKCG+J@TLDLp WJ Df ê E@/7MG .¯P«RC{T BL RLT BL G*WRCJn}T nnT WRLG0DLT J pnT DT B ¯ «ÝT¤pGGRLTw ¢8G+p§@=CTf pG+D ujJ0Jf{npG G.BLp 9nKCG+Df p @ { Jp (J DLK ppnT ¤£J {J LnG$¨aT KCG {GG8Tãt{GGKCT 3¬cjD3 WRLGA RLGT {@ ¯ 0NG WJ ¥G WRLGn Rf JfD p tOCBCJ p¥>TJ0RLG+J£ @..GpT D3Jz? J {tJp £wJf{J LnGN pT¡G ujDf pG uJ pGK TLBL D WRLGC{GpG+DLGTJ4pnTw@ {T WJ pDLNpT nn pT D CJ¥ L{T BCDLK T DLp pBL pGKD WRLG.nLR ..GpT DrpG pTL*9RLn_RN§G+C{GpG+Df p0F J upnTw (£wJ {J LnG Ý9RLnG WRLGRLG+J£ @ OCBCJ p¥7n pD pGLpJ pGK.D JzJ*CG WJ uT ¯«RL8+J D¡GA£ nWBCJ= <GK( @JuWBC.DL7 WRCJ WRLGpTfn pTLDf RLG+J£ @.GuT DCTLBCDLK¤p@Lp pG+ nTLCT uGKTJ0RLG+J£L@OCBCJ p¥ pn p pDLJ z WRLGATL{n D¤J DLKJ7nn R J Df pnOPBCJfp¥7D3 WRLG9RLG+J£ @..GpT D [ > .T£LjDL>D. WRLG9CJ¥f {T BCDLKTlJ*pnTAn@{T WJ ujDL7uT n uT DH¯ «ARLGRLG+J£ @rOPBCJfp¥( WRLG+Drn0G¦G pn£ Gn@KCGT BCLnGK4 {TL WRLG.pTfn pTLDHpTn 7.JWCG J pT D WRLG n.n < ¯¤«ARLG+§GT §G J° J 7J0 WRLG¤§T WJ pnT D.Tf pnT DT WRLGpT nn pT D4n0T DLG+uDLGK WRLG G¦G pn£ GKCG {GGTt{GGKCT . WRLG3n Rf J Df pnOPBCJ u¥$D4 WRLG(RLG+J+£L@N.GpT D WRCJ 0TLBCLG. pTr WRLG pT nn pT DH¯7«ARLBL*T DLG.+J D( WJf¥G0 WRL] G {tJp £J {J LnGDr WRLn7p@Lp pG+ pT ¡G. WRLG0nn Rf 0J D uOCBCJ p¥ > DLp pG+JK4T WRLG.9RLTfGRLG+J+£L@= GpT Drn ppG 9J7D WRLG ,AE Ln WBC{G¤BLpGK4jD C ¯.y 7n0& J {tJp £wJf{J LnGD$ RLG0pG+DLpG. WRCJ A WRLG0GLn WJ pnT DrKãBLG. pT WRLG T pnT D(Tz WRLG0pnT £wJ {J LnG=¨ WRCJ An7 pT WJ@ C WRLG0JKCjJfCJ pn{Tf WJ pnT DT WRLG7pTfn pTLDC¬An*T5TL{KCG+ ê ; ! " 9RLnnG RLG0G+DLG+{ @WLnn p pDL(T WRLG pT nn pT DfJfD pnOCBCJ p¥rp@Lp pG+%n0TT {KCG+ !" # 9RLn_RKCG+¡G+DLKC.T D WRLG. pJfDLK=Lj% D $ J7GPLJDLGK CGnT0¯«ARLnz.G+J DL RCJ RLGJKCJ CJ u WRLGT {G+ S*RLR>p WJ uG WRCJ WRLGÜ Jp KCGL{GGTC §GGKCT T Df pD BLG8 pT7{G+JD.T D>n pWDCJfLWRLT Gn G+DLp WJ pGABC. pT7J7CRCJpG0+J D.¡G9BLpGK. pT7T L WJjD.J7¢8G+p{@ CTf pG+D ujJKCGDLGKD WRLG7WCJG7T WRLG7pnT £J {J LnG T ¯ [*G7WRCJnWRLT CGnT0C WRLG+§G7*J0nT uG J DCJnT f@= uT( WRLGRLjuJzCJ$+Jp: G Dê *RLG+{G¤JOCBCJ p¥!¨ tJp 7£wJf{J LnG+¬0.T£ G7D4 WRLG¤CJ¥ L{T BCDLK êY.
(64) ãGnKNTJ({Tf WJ pDLpT nn pT D!¨apnT £J {J LnG+¬¯ 0NG0RCJnGPLnT n 0 RL0JfDCJnT @$DrpLn @LDLT BC J {LBC.G+D ¯ «ARLG(DLG .p uG+jDTLBCJf{ BC.G+Df 0n pT®DLK! WRLGWCG WuBC T9 WRLG&{tJp r£wJ §jJfLG® [ !jD WRLGpTfn pTLDLCJ_¥f {TLBCDLK uyse { §T WJ pDLN RLG=uT n uT DH¯ «ARLG={GnG£J D $CJf{ ¤T0 WRLGNFJ pJfDL J DD £ Tf£LDL RL2 G [ ãGnK +J D!¡G(T L WJDLGK @!{G+LJDL 8 f@ RLG( p.GtDLKCG+CG+DLKCG+DL pT nn pT D¨yRLGKC G+RLT L¬8ãGnK 8 D$ªOH¯Z.¨ Z ¬. > >. [ [] A D [ +[]
(65) T
(66) 8 8 T 8 7 A G+G+G & % D 2. . ¨.@ ¬. «ARLGpGTLDLK0 pG+p Tݨ)@ ¬}nJ D*D uG+pJ pnT D° pG+p 9RLnR7+J D7¡Gz9§ u pG+D*D7 pG+p TC WRLGnpT WLD > J DLK WRLG9J DLLBLjJf T .G+Df WBC %}T WRLGAnn Rf KCGL{GG9Tt{GGKCT ® > D3 WRLG9RLG+J£L@¤.GpT D9#B ê E . [ ¨.8 ¬ > G % &. ¨.@/ ¬. 8 + %*¨ ¬8 % +8 ¨ ¬. ¨.@B ¬. ? G+DLG WRLG0G+DLG+§ @$Gn G+DLp J pG0J {G>Jpp ãGK! @r WRLG $®tWLDT > $ > A %¨ {G+Jn WRCJ WRLG(RLGKC G+RLT $®tWLDn <G+§T ¬>An WRJfDNG+DLG+{f@NWLnn p pDL c9RLnR.T*T {KCG+ !" # ¯ «ARLG*KCG WJnnGK(+Jn+BLJ pnT DL*T )¨ 8 p¬8Annl¡G7KCnp+BLppGK(J pG+»` ¯ 0 RCJ GAAnWR uTCTfjDf T BL ARLG+{G n. WRCJ 7 WRLGD pG+uJ pnT DN?*J .nn pT DLJ DKCTLGDLT ] ppGhG r WRLGT pLn WJJ DL BLJ >.T .G+Df WBC T > ¯ «ARLG+{GyT {G7 RLG7T pLn WJJfDL BLJ A.T G+D WBC *pG+CJ uJ pGn@¤TLDLpG+{£ GK¯ 0NG0DLT {Tf WJ pGA RLG0RLjuJHãGnK$An WR® WRLG7pnT £wJf{J LnG %*¨ ¬ DªOH¯Z¨.q ¬CBL *nG+J+£fGBCDC{T J pGK( WRLG.RLG+J+£L@f.GpT D3ãGnK [ J9C§T CT uGK=f@(M JfDLT RCJ G 9J¯AB ¯ «ARLn7T Df WpJu p9 R$ RLGOCBCJ Df p= <+J pnT DC{TLGKãBC{G.T # 9RLG+{G. WRLG][ ãGnKNnJuT {Tf WJ pGK¯ «ARLG*KC ¦lG+§G+DLG7 pBLp J>J p uG+cTRLT T ujDL° uJ .G+f WRLGAyT p G+T p§GWCT DLKCDL. pT> WRLGS§T WJ pDL DLG+{ pJLtpJ .GJ DLK0 RLGJ u pG+ uT9 WRLGRLG+J£ @f.GpT D>{Gp Ý uJ .G ¯ T RªÜO¯.¨ @B ¬ÝJ DLKªOH¯Z.¨ q ¬» WRLG0FJ pJ DL J D+JfD$CG>9{n p pG+DD® WRLG*TLp. > >. . % D A D. A . A . [ [ [2[] 8 8 8 7 D [ [
(67) #
(68) 8 8 8 7 D [[]
(69) T
(70) % 8 ¨.8 8 T 8 W ¬% 7 &. ¨.@E ¬. A % 8 % 8 # ¨ Y ¬A % 8 %U8 # ¨ Y ¬% 8 % 8% Y % 8 %. ¨.@W ¬. . a*G(JpBC.G WRCJ . WRLG(CTLBCDLKp J pG>yT p.GKJ . WRLG¤TL{n DNT* WRLG¤uT n uT DJKCnp+BLupGK @ 3SBCuJDLj¥3G AJyG¯ B WRLG+D WRLG*pGT DLK$JfDLK¤ WRL{K( uG+p.T5ªÜO¯A.¨ @Ef¬£wJfDLRH¯«ARLnA+JfD¤¡G7pGG+D( @ WRLG*tJ A WRCJ 8. 8 ¨ Y ¬ 80¨ Y ¬ . %U8. ê ê.
(71) . 9RLG+{G8 WRLGz£JBLGT 8 # J . > >. Y q8 # ¨ Y ¬H ê RCJCGG+D.BLpGK¯«RLG+D7t{T WRLGz{GKãBLGKFJ uJ DL J D. . % D [ [ T A D . [ []
(72)
(73) % 8¨.8%8 T 8 W¬% 7 . ¨./ Y ¬. WRLG7Df pG+pJ pnT Dr?9Jf.n uT DLJ D(+J DrCG>T L WJDLGK$J. [ ¨ ¬0. % [ %. 8&. ¨./ ê ¬. y pGG+ kDCJ WBCpJ} pT0 WJf¥G %9¨ ¬+! $ $c pT¡G9 WRLG*WDCJ LRLT GfG+DLp WJ pG7J 8 + ¨ ¬L9RLG+{G]! $ $nAJ D G+DLG+{ @(Gn G+DLu WJ pG7Tz RLG0BCDC{T WJ ujDL(RLGKC G+RLT 3pT nn pT D!¨{X h h ¨ Y ¬ ê ¬¯z«ARLG>G+DLG+{ @(Gn G+DLp J pG TQ [ ¨ ¬ÝG£ T n£ GzJT §KCjDLf@JnT DL7 RLGCJ WR>KCG pG+u.DLGK¤ @> WRLGzDCJ LWRLT Gn G+DLp J pG ¨ ¬cBC pT(J¤CRCJpG ãfG+DLG+pJ pDL(J¤¢8G+p{@CT uG+D pJcD¢zTLpDf CCG+DCRLG.G+.J CC{TLJ pnT DH¯*«ARLG¢8G+p{@ CTf pG+D ujJ+J D WRLG+DrCG0+J+BLJ uGK$D$J.u WJ DLKãJ {K(AJ@. . . $-% 8Z! !!%$ $. $ !¨.% 8 %8¬+! $ $&. ¨./@ ¬. « RLGA¥G@>yG+J WBC{G8T WRLnC{T GKãBC§GAnz WRCJ c WRLGA¢8G+p{@CTf pG+D ujJ +J D3CGA+Jn+BLJ pGK3jD3J7{GG+§G+DLG A p WJ pG2! $ $H9RLn_R.G+JBC{G0DrtJ RLT WRLG $(tu WJ pG7KCGDLGK!J 7 F Y G 0.n GKKãBC{DL WRLG JKCJ CJ u0§T WJ pnT DH¯c«ARLn9JnpT.WRLTA8G+Jf{n@( WRCJ n9JfDDLKãBLGK$LJ BL G9¡T pG+Df pJHT BCLnGK$ pT J.pnT £J {J LnG09RLnRr WRLG{Tf WJ pnT D3T WRLG7pT nn pT DH¯ [7D(GOCBL£JnG+D 0CBL 7.T §G7jDLu WpBL pn£ G.AJ@ pTGCRLL > WRLG0¢8G+p{@(p pBL WBC{G>* pT¤§GKCGDLG WRL G [ ãGnKDrWBL_RrJAJ@ WRCJ A WRLG.{T WJ pnT D(J W§n % J pATLD( WRLG.RLG+J+£L@$.GpTLD3ãGKpJ WRLG+ WRCJ DTLD WRLG7pT nn pT DH¯FHG . [ [-% 8 [ %. [ &. ¨./@ ¬. Tw WRLG¤J pnT D®$9RLn_RrnJOCBCJ Df WBC .GRCJ DLn+JzFJ uJ DL J D®TL* WRLG.pnTw £J {J LnGs%*¨ ¬k CGTL.G ¨Kã{T CLDL¤ RLG0C{.G0T0[ ¬. . . T A [ [ «c [!¨ % 8 %8¬ [ ¡ «c [ [
(74)
(75) 8 8 T 8 7 . «c+¨.% 8 %z¬
(76) A G+GG.
(77) % «c. A. . ¨./q ¬. 9RLG+{G3GRCJ+£fG¤DLT {Gp uT {GK WRLG(¥ DLG pnG+DLG+{ @N pG+u T ° WRLGpnT KCGL{GG¤Tt{GGKCT An WR RLG¤.T .G+Df 0TDLG+{ pJrTA WRLG¤{Tf WJ pDL$uT n uT DH¯(«ARLG WRL{K pG+p%T¨./Z ¬*D £ Tf£fG DLTr p.G KCG+{n£wJ pn£ G0J DLK¤RLG+DLG*nkJ>CT uG+D pJ}9RLn_R3GAKCG+DLT pGK(J ¡Tw£fG9JS¨ [W¬ÜT D.9RLnRGAnRCJ£ G .T §G uT¤WJ@CGnT0¯«RLGpGT DLK pG+p%+JfD=¡GnKCG+D uÆãGK J9 WRLG¢zG+u{@=¡T pG+Df pJ9RLn_R n£ G ê.
(78) WRLGWJ .G J.jDªOH¯!¨./@ ¬*9RLG+DC{T G pGKT Df pT$ RLG $ p J pG ¯$«ARCJ 0 WRLn.nKCG+D p ã+J uTLD pG+DLpLnG+J DrCG.pGG+Dr @$Jf¥ DL(J D$J DCJTf @( pT WRLG>_RLpJ5CJ}¯³D$ RLG0+JpG>T WRLG0RLpJCJ KCnp+BLppGK(] D ê f WRLG9JKCJ CJ pn7_RCJ DLfGAT WRLG*W¥ @Cp.nT DH %*¨ ¬nDLT p¡T pJ pGKD WRLGyT nnTwjDL FJLpJ DL J DH. . . :
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