Luận án phó tiến sỹ Về các nhóm đối xứng không thời gian mở rộng của lý thuyết trường lượng tửLuận án phó tiến sỹ Về các nhóm đối xứng không thời gian mở rộng của lý thuyết trường lượng tử

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BC p~ BOC.TRtING~HQCCEUIENNGHIEPVA D~ NGIm
mtfdNGB6I HOC TONGBOP m-AMIm6 BDad ETh'E
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n OAe EQ( J)OI DG IHONGmm GUIi MO.R(8G
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c.1l1V"&nDganh V~t ~ 1y th~et -I:a hitu 10201
!DImrPROBOem .IE - 1966
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cq trim ~ hoc Ul,am~B~.an V&tJi Ji thwet
ihoa T&t 1i - ~ h9O ~6Ds h~ ~~ phS Jib -Chi - KiDh .
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IDl\IDg ~C11 h~~ dAns
If~1n 11690Glao - Giao 811I. PhO.tUn sl.

DucmgTan P1d -G18.o all It TUn .1.
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Ng\fO'inhen xet 11
u~ ,~en xet as
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CO'qUBn nhen xet,
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L$ an se ~ bao vi tid gOi d:~ng chlIm 1$ .8n Nha
n mc hW t(l1 ~ ¥ h9c ~Ang h9$>T.P. JIb -Chi -J4iI1h
vao hbi nga;y thq nibn 1989
Co 121' t1m hiAu lu'n an tCl-i !lhll vien 'lrIICIngd:~ h9c
Tang hC1.P~~ phS gb Ch! I[~ va t~ ']hit vi~n Q~c
'gia.
.
a
fIij fJlu
.
lincm doi ~ khcug ihc,i glan can ~n nhat Qua 1;
thUY6t tI'lZCmgluvng t& tU'C'ngdot t{nh la nhoa Poincare" .Doi
me; Poincare xu§:t phat t~ quan ni~m v~t ly cho rlng khong
. , ", ,
thai gian cua ly thuygt tuongdo1 hiP la dang nhEt va d~
hll6ng, vi vb cae d~c trtmg e~h~ lll9'llg t~ khong dU?c
tbay d~l khi tlnh ti~ bo~c quay h~ t9a dQ ichong then. gia.'1.
""
lfuo~ P01ncace co 10 tham so, cae vi t~ Qua no la ceo tOaD
tu. 4 - xung l~g Pp.va 4-j;enXO'1110men xung luvng ~;"V.
, " '
Nhom conformal Ie Mom d01 Dmg ch~a Mom ioincare
nhu mQt Mom con. h"homconformal la nhom co 15 tham 80, cac

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vi ill cua no bao gam 10 vi tll cua MOil.poincare V8 ngoa1 ra
", "" ~ - ,
C9J1 co vi tll D wong ung vc11.phep bien d01 co den tO8 d9 T8
KjA tlJ\;1ng ling vai phep blin d~1 conformal die trllllg. Nhoc
conformal Is nhom r~ .nhSt g1lt ~t bi en hinh non anh sang
G:i.~ thUt ~t bien conformal c, neng luvng cao d~c cac thlJc
ngb1~m :tEh1Xf hptolD-had1"Onpbi <tan t{nh S8,U :mc nh~n.
ido. r§ng nhom d01 ntng Poincare b~ng ~ch d\l8 VEtO
cac ph.p bign dAt doi xttng 'Ych cac tham 85 spinO' dan den
Me):; sieu dot x~g. 'Sieu dO't Ding ket h9'(>cae truang boae
,~"",
Va ferIti vao cung mpt da tuyen dot xung va do do .dan den
MUng khe Dang to ldn d~ xay dlJng ly thuy't tb6ng i:1hSt c.ac:
, ' ""- ,
tllO'ng tee cua cae b,t eO' bBn. cae ly tbuySt traong .~~iu
d6i ximg co mpt as t:!Dh chat 1; tbUI SO'phin Q g1~11 1'0 rit
so vGi cae l;tbuygt kbong siiudO't %ling tm:m.g ang, ob
, t, Ji, .~ '. . J-
~t beng 80 ta1 dhuan hoa h~, tat ca cae gian db vong ~
.
vacuumtr1~t t1eu, trung binh Tacuum CU~ tenxa n!ng
luvng tr1ft tieQ v.v HIe ~Iu cae 1i tbuyft 81~u
%Un«
dS1
J
~Dibg~ Db1'~. A-~a1-C1.i'-'~,'t v".4'11 Jf;Q-ch* c&.
~S ohq 1;12,,",D&b1,. rO r~g chaing II:i.Dh.Uu.~S1 Tlj,.g
.' . . .
quA1;121101. qlq 1uft Quathe glat 12.1,octbb, ~~8 ,.

giG gh 4'~Dh'~ DUt'th1,D r~h ~1't1 cgng trbh 11 thl1ye1:
Db'. 11&. hf .1,~o dd1 =g -v6i tbltC 11~1i. c~ vit 1i h~t
Ilguds. ta olio rh8' s1iu 461 x.ing ta 161 thc1a' - 'th,. chi
h1fn 11&~Ii dU1 Db(t - cbo mic v~ d'a' J18l1gt4J. aliA 11
tbu1it th5ug Dbgt ~wng taer' Steu d~1.g' si'
BP dit m§t
trft -1:\1.0 do trons ph~ hOt, bOb chI ad t12ams6 tdl y cqA
04C 1; thuy't tbSD8 Dhlt,-s1&u d61 ~g co tb~ .~~~ quy3t
dUVc kIlla oph ~ thuft' Qua vh cft h1e:tuc07 ~~~. 1i .
thu1'1: 'boD« Db't 1cfn (gred unU"1c:atj.on)-, V.V .0$0 1f
1inttyet1:12&Dg.«, t~ t,*o 121fl14.1 ~4t ~" ~iiu hS~ .
(supergraY1'ty), sUI1 day Csuperatring) diu "flu d\P1C ":~Id1ai
f1" .
thee y t,aoDg 81@a dQ1%Qbg;
,BAn luin in J)gbteD oaia,DJQ'tsS 'vCn cD ~gquaDh c&c
Dbol\401 ~g .; r~, n01 trill. Saaetay '1. w.t#.~ cae v~
. 4:8 d1 8a11DgbUn o. cae, ~~t qa&'.h c~ tl<; ~~I. -'
~ 8*t hlnh th1io lup 8f.eu'th~ gtp V$ 81h
1;ruWg 0u1 8iiu 481 JOing~ r~ng k't hgp -vthCt81 xUb'
trong 30(2). DUngpb~})thalli '0 120. ttt{~ bcrps1.~u-~*1Ii.2t
vin 4pg phllmig phap 0$0 MAtt U3n cA. .t1~-~ .clc~ .
Salam. do gt.a di tbll d. qQ.yllift b161 4A~t~y d~ c cic
'toe ~{, 81&u t~6 cang -Dba t:rutmg 1;hAJJhpJIb dft ~ ett~
J)hep'141114&1cd 8U~ 4&1- rJ:, l'QQgsQut.
~ WghUno~ cae "1 11811he gLaa c&o~ ~~
phb o. .~t den cis tnyen do cae 401 12014~t -me lip.
tt'O11g818u c!~1 x.mg rJJDrQ11gsu(2). %81818.11tratmg If . 2
tAng quit, vG1 gta tbuy't 't1'pS th41 ftOU\l1l 1141 b1ea 81~
461 =s .) r~ng. tao gt8. tha 4Il11Ooio It' th~ glia do hlJa
tUQ'Ag!paD_t 411. owl 0&0tN(,q tb$mr pItIia.trong sUa.

bvo.s. 2 t6acfi-t. . . '.
4-
-> -'
- Xh1o .at blim thvc lup 81eU kbong glan bar80111e Va
.Uu t1'llCmgg1a1 t:Ccb cu8 nm)1Iitac gi8 (;olperin. Ogievet-
xk1 vA cOns 8¥
- blM tbiic lufn c!1tVCtbw nhin 18 raOta day-c
dl1 a~ "'~cblt Chi nb't cac li thu;ret sleu dol xUng';' r§.t:g
Ii ;; 2 cbUa 481=g trong SU(2). JIbe, hlnb tbde lufn ~;rtcac
bn>ermul'tiplet cU: s1eu dO1 .JJ. 2 chzqe 110 1;. bO1. cac
s1€u tralmg tU1 t:Coh - cie 8ieu truang kboag bt rUg ~Qc
bb1 cae di'u klin
hincbe cO t:Cnh ch!t ap dlt. Do do.' d01
vcn eac sUu tr~g' gial ticb. co tb' 8P dpg phuong pbap
Jibu steu tm~g. tAng <iUAtd~ tbu c'c 'hi ihac l1'n hi cic beB!
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tllO'ng quan h.l diem cua cae t1'llC111gthaw pbb. ltet qua, tac
", ; '". J
gt'8 tbu d. cae 'bi tbllC g1ils eae he. tvcmg quaa.ba1. cHell
"; ~A-_'" . ,
cue. cae t~ thanb p.bln trOl1g .cae h)'perDlIUplet J'a;ret-
Sohn1us va Howe-Stell - !oWD8end.
" ' ,_if if; ,
- Xhao 8at viic _t hvp dQ1 DDg conformal TO1. sUu
doi mg th@h dol :dng rOng h(l1UDot =g superconforllBl.
~~c ~; neu V$ cllling m:LDh minh d\ sau v\ tiell cbu~ hl~p
bien' 8llperconforml: Hlu 119.t Lagrangian slell do! Ding, v~
dang thC1. le. b1~p 1:d ~ conforl!lal tbl 1; tbllyet; le.ld~i Dng
superconformal. DUng 1 v{ 41\1II1Dh b9a, tae gi8 xet d nh
bS:t bleD conformal va superconformal cua aO hl.nh TO hu6ng

sih deft :.Ding vcn tv tllO!lg ,tee gs3 .va 88 h1nh dieD dOng
l~c sielld01 xttng cuB 188S. Zumino.
a" %" .1-,-"""
- De t1111h1el1 cae die hnn cua cae 11 thu1et trao-'Ig
" ~ .'-, ,
co dol :nmg eonforll81 va 8&q1.r83formal bt pba Ta tv phtd,
tee 818 .i d' xuSt va kb~o Bat 1110binh 11 tbll1't trag
' ' .,
trong siell khanggian (2,2) co dol nmg 8uperconformal b+:t
pba va t~ pilat nhc, t~D tf1 nghl~1tt c~ c:l~n lo~i l.nstanton
t;~ pJt~ tthl~ t~g 6.pha r"s va tv phat d61 Ding, 80
:;
hUb. .~ ta cae fhlDs c1Gs 1IIfIt8to"& aO1;~ bo~ v~
aOt ~ :tera1ont\tcmgtaa D'tiauaft c ~s~u 4~1
miDg. Ph1lCmgtrlm ~t~1Q11 trong .~ inatanton
. 1_0. ' ." , 11 ,
cua boeQl1 CAP D8h1faa ch~ xac 9'a tIlc1Dg \fIIg <tin IIode _roo
~ .
cua :tera1on.
, - , "
Cae kIt qua cua tae gia Ita. dktgc c&ng b8 trong 5 ba1
bao tran cae t8P Chi. o"Terpchi T!t .Ji", "Czechoslovak
Journal of P1Q-jics", "~eng baa ihoa h9C Dp h9C tADg hClP
~8nh ph611& Chi 14inh" (xem b~ danh JII.\1Ccae c6ng trlrm
GOngb8 cua-tae gi; theo 4A t8.1 1$ an 0, eu8i ban tan tit
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ntV).
Ban 1* an, Dgo81phh .& ~u va k't 1utn, CO5
'1 "
chU'ang, J php.1\1C

J t<mg c~ g!a °113 trang", Sau ~ 1a n~1
dung tt. tat !cae Ct.oIc1Dgcui 1uen an.
+ +
+
6
Cb~g I
, « ~,
mfOjt001 D}.riG,POINCJJiE
n'clc ilf R~rm dA 1;0
'
;fJJ\
Ch~g ~ mane die trlln~ uhf!' mon V$O 11nh "vc
ne,b1& c~ trong &) ~~ Sia tr-lnh ~y cae kiln thuc ca b6D
v~ t:b&I d8r ~ Poincare \Fa cae ',1DC1rfmg clla no I 1110111
con:f'o.rmel. %thom81311 d6i Ding vA nh~tn auperoonfor~81.
,~. , 'A , . ,
1 ~~J?o1nce.~: lbomPoincare t <>ngquat P 1a Mom
'tIt ~ ole Ph~p bign d~1 tw98d~ co dvng:
V '
, ~- I\~xv +.p (I.1)
'trong do
~ 11 1.119.trfn c~ pbep b1Sn d~l Loren t6ng qUt
~,\, 1e Yecta tbh uSn 4- *98 dQ. Ibom Po1Acue htPP~ la
Jabomcon cui P @1I~e phep bi en d~1 (1.1) 61. ~etl\. 1
va ~~1. 1h,6Ephil Vf1l n8ng cue MOlD Po1Jtcare hfP ki h1fu
u.~o' T:i.en ~ bS::t bib tllO'ng dot eua lith uygt lU911« tit
# ~ ';0 " .
tLlO'!lgdQi tum d. phatb1E!11Mil 8au: ,"V()1. phep 'tie clol
Po~nca" htp, v.cta treng thai bien cfAl thee bl~u c1dn
~ ' . ., Ci>" .,. ,

u~ 1;a
Uh t,c cue ahOmcJo. Pi" la Dboll 10 them eS,
Vi t~ 1i. 4 vi ta tb;m tUn va 6 vi t&i quay.
,
cae
,-, .f,\" , '
dall 40 -c,agi8 trinh bBy dQi 80 cac vi tll. cue JIhOm
rQincare, phUO'J1gPh~p pn6n 1091 ~e bl~u dien bit Cbs cIQ.J
, " ,." A."',,-
1
t
cue dQl so nhC)1,P,1h ~ cae gia tr:1, rieng ,cua cae as II1r .11&
,
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2 Cae Sp!nCf Loren t Cee spina la cae yeu to cue lchuJ18
t
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$ian Tee a phllC he en ~U th\1c h1tn o1eu d,i<311 <:<:"80' cue
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nhq~ SL 2, C) (Dbom pbu v~m nang cue n}:),QIt;Loren r.Ung L
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CO hal khong gietn bieu d1e1l khac May 't~g ~ v(;i ha1

- bi~u d1'In 1Ih.ang.'t IIO'Agduong cue SI,{2. C) , do 40 cO .hat
10fl spinal 8pinO' oh1ral-'t~1 'i~!-;6 khaaS- ~-d;i;)'~ ".
sp1nO'Ohiral phs1 (oh! 84 cO eft ). Cae eptAO'ha1. thUh
."phlD do <111110"891 11 cae spina \Yeylvi (flu Ueu cSuve 'fe,l
3 .
duzagde .a h nO't1"1D6.
DW1pbip nstJJch If~ toe. 4~. spinam cbi e6 k!16Dg
ob«. tren ct1\1,ln thanb ~tDa '9'c7tchI ,88 cO ch& da!\ va ,
n~ 1,t."£I~Tiftpbep
btln ~~1 00 t{Db e1tft l!-6 c!uO1.
dfDg lI't phep blln. <I~1 tuy3n t{Dh, cb gJp <101 sO chI'"
. ""."" """",,::
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biE;U dlen Va kbao 8at ceo spIna 4 tb8Dh p~ ~p:1J1O'.
hong tNCmg bvp tADg quat bt8ptDa cO 4 tbUh phh phtic <lPc
Ii-PI day la tr1img b9P cae 8p1DO'Dirac. 111\1 b& sung them
cU.'u IclVD tbU'C llajorana 1'c;r C 1f'T .'t' 9 tbl Qua' co 4
thanh phh thyc <lQol0p (spina. Jajorua).
J BbOID819'1 461 ~t i)j .;. rOag !tho. 441 ~ 'oinc-
an ban"cSlu DgWt1;a *l~ Dbo. G obaa Dbo. Poincare,,;" UJO1;
, "," " m A , " )1 '!Ir
Dbom do1 X!.ZUghong %1&0. cSOe. "'IA! nh1en haong nay 69P nh111'U
'boa Dg,1. Sa'1 do :m1t hip cac. cI~ Ii DO - 40 :a;c liP
t "r~g cac clot hot v,t Ii t~ng qqa1;Dhlt_hJD dl' 01\1 trac 0:
~ -G chi co th4 Ie. t{eb trtIc t11p cua nbO.>f1'otncaft v~ IIIlOm
\ .
cl61-xtiag trong. ,. d ,.,.,
Iuy Dbien cOtl1l d1 D hOD*c c8c11ad ~ ut
"" . , '- ,
cac %1<1108GIdt'angpb81 la cac nM. Lt. thm.S,.m:mg - 1&

cae Mom Lie phan biG (graded). Mn cOM cac" Y1 ~ ~ ;.
~" CUB Dboll P01noare (thu9c pha. biG 0 '9'4 cI!IIJO&91 14 cae
Vi t-i ch~n) dua them cae 1f1 t~ $piDC1(Ct. . Q. Hth*
pban ~o 1 .:.' dJ.J9'C~1 18 cac vi 1;~ Ie). Dt1' as ma rQng-
, "It 9 ".' ""
g8m oa giao bon tit pttan g1ao hoeD tu. lChoa tmmg tJD8'tCi'1
ct;1 aO nay dll9'C ~1 1.8 nbO:mdeu dB! xUrig;
8
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6
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Sau do tac"l1i hum bay ct.i 8 vi tl.: cua nholn s1€\.<
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dOi Dmg. phan 1001 oac leudieDuat tha quy cue d~l EO'
~-" , ,.~
bi
&
c1
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slc¥ 401 xung. vaG eu ten cua del 80 nay co net d~c Di~t
"1a ca'; boson va cac :fermion n~mtrong cims m9t sUu da. tUJ.I~;J
va cO cims 11116:1luvng.
s~ "'- ~ .
4 ~ieu khBn~~~ - i~ t.rsmpg: Lrongt;Leu III\lC nay
teie gie. trlnh 1187hbh tbalC 1. ~81eukhiiDggian Y8 s1Cu
tmang dot vc11 slall doi %Ung III1nl11a1 vat 1 vi t{, splnO' (N.1)-
StEIl kbang sian ls kbqg1an m&rSiDg cb.m cac t08 d9 khong
thO1. g1an thOng thuDon.s . va c&e toe d Q spinO' ph8n €1ao been.

BUu traang ls cac 'tzuOng ne dpm trang SUIl ][bong gian.
Hlnb th&ic 1ujn. slau traOng cho phep mOt~ 89n gbe . cae eta
tuyen slell dol' %Iing. 1.egrangian b(t bien, 1i tbQet nh1'u
lofD b(t bLh n cac guy tIc Fe7D- cO th~ phat b1~u trio
.Ugp
tbeo ng& ngii 8:!.e~ truoemg. ~
.~ .
5 Jgom con1'orMl: 1Jbomconforlla1 cu8 kh6ng thO1 glaD
, ,~ .11
18 Dhomcac ~ep ~~ d01 't98 d9 bao g~m:
- cac phep bi&n-a&l cue MomFoincare,
- Phep Mill dA! co din toa dQ ][bong thCn. g1an
,
%~ .~% . ~> 0
~
- Phep bl.Sn etAl eon1'orma1 dIe trung
~ .or.1{xl (~ -~ x2), tT(-x} . 1-= c2x2 (I. 1)
lIhom conformal co 15 them 86. cac v1 tu. 141'i1,&\'"~\
D
, I
va K}\. '
Sau do tae gi~ trlnh 18y d,1 86 cao vi tal, gisi
thIGhvat Ii oao pbep'b1fn
et~l (I.2) ya (I.3>,.tr1nh b8y
, II Jt I-
phuO'Ag phap cae bieu
dien cam 8inh cas Maclcey, Salam de
II A L a .,. III II'
ao dtnb quy lut~ bi.u do! cna toen hr tmcmg doi YC1 cae
, !It_" .,

phep billU.l 401 cua ahom confer_l.
(I.2)
6. - ~O. auperooafo~, 1IItOa~omu. 1a
0- .ahOa00a1'01"881 oa- cia- .~ T1 ~ 8p1AO'.
DI too thimll do1 .& kla ~ ta pb8t t1tb yao 481 a8

S
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ooafo1'1l812 n tw ap1DG'. ~. fI.c'" mOtvi. tll vo haons JJI/.
cae hi tl m bop YJ _0 .tJtb cf4184 8UpU'OOllfOr8alII.
trinh -7.
Cb U.
sIiu WI XIfBGJ! ROBO .'
d:r YCh~I ~.~ (2f
" II'" *'.6'
1 C"'Q nhna at an ~. 1 "Zm'Ia' ~ ' JIbc)aaia. do1 DD8
-~ *'.,
t nnh bay acbuung I la 110'*g aptDCt be Dltft cua nhOm 461
mag Po1ncar ~ &91 Dbo. 40 18 81eu 481 -11.1 (I ki
h1.jQ 86 1 1a; spina). cO thi .0. r9ag at cao Dho. 81eu clSl
~g all;. Jl vi tu. &pUla (Ii> 1). ]flu 117 »ft tg sp1Da @ 18
bilu d11a fXI8b c~ clSI xUng t1"ODgSU(]I) ta 00 cfel s4 81811
., *' . ~ . '~. *'
dot XIIIIg110'rOag t hVJ»IIOt each kb&tg tIa thl8mB dol ~
khong thCtt g!.8D va 4ft =a hong Sf (]f).
.
I
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'fruimg h9P 40'!1 paD JIb t oua 818u QU~D1Dg , rOD&
18 trWl1g h9P steu cI41 Dug wb rpng kIt hgp Wi <!61 :a8g

trang sue 2) CdS1
~ Isotopic). ceo hi u.Rc pb8n giao hoD
.,.
(
.'
1
I
Qua cae 1 tal ap1Da Q()(1 . 1~1. 2) t%'Gag t rwag hqp co bch
trung tam 00 dong:
tQo<.18
{T; .
Qfi3 }
Q':j ~
/3 )
21 ~i~ ~ecp Z, (II.1)
Ii -2ieU e 1l', (11.2)
~;S
j -
. 2~1 (vf~ ~. en.)
) j .
l Qed' ~ ~
/'=' )
~
~t b1lu G1b bit kbI qQ7 cu8 do-1 at) aie\:! (!ci ~
" fI! 'fI!
merr~g SU(2) ~~ die trung bi11 khu1luogngmVa , 80 l\l9Xlg
" " '" If! '
tllBuperspin Y va Buperieospin~. cae da tqen dui - xmlg .
50"(2) tbazang duvc g91 18 c8c hypermult1plet. CII\.ttrUc(3, I)
'A J. .,. '" to

(8
eas JDQt bien dieD bat kha quy Db., Bau : spin, I,1soapin)
(Y,T + 1/2~(Y,'-'/2)E9(Y + 1/~) ~ (Y-1/2,T).
2 SiBil khon.r u-iAD- Stell tr.Km~r Steu Ichong gian lID
r§ng t~ ling ven sieu dS1 X!ing SU{2) co cae 1;98 ~~I
{x}'\, ~i t-e-l} (1-= 1,2) (II.4)
81&\1 ~-raCtng H = 2 (Tilt t&t 18 2-sUu t~) dlZQ'c
r .
%80 dtnhnhU" UI. . .'
1 .exp(1~ ~* e:q>{-1 (ZZ+ zZ-+'J exp[Hit"S +S~}]J(
.eJCp[i(~Q1-GvJ~(o)cxr[-i(qG+G.¥J]" (II.5)
expr i(~S S-iJj exp[i( zZ +
zZ+)Je-xp(-i.)(J'4~J 1
trong do ta da 4n Teo cae.Q h1iu Bau d~ phan biit 2 vI
tlr spinO'.
S !! Q , 8.!!
co( co(~ CK.
.lJ ~f .A
voc.::' .vo( , v~::.
va de r; h1fu
-1 Q
QJc " 0<
- -2
Q", 2" Q.x~ Q < , (II.6)
- - 2. - -
-6-';'i, ~ = -&"" ~ 2tX E -f1,;.,,
~=<j>("$.,f)-'~"ZI'f/"Z) ,
(leo)=- tp(O /0 ,0,0,0,0) .
u ;.7)
J Qpy

1ait biSn dAi d~ ,,' . , (II.S)
., T U oftUAe4e .fa t:'
}Jam trm7p~ toRn 1;~ dot TM MC n" p. ruoarw T~
sUD. dot' , ' hep big~ aA1 eU4
""7I'1D'ilia rt)J1' SU(2) :
0
"'
.
'"~"""-

'~~-~.' ' '-'-'-
i
""
nAIIJ""f' 'f/Ii."> I""""" .
t;r',I" f,-'! J.Ij!.:'nU~ij
"c'
!
"'r\"""\
N
f'~"\,.~.,i
I
""1 \' ,'. "", .Ili. !
11i\.,:It.:~:h')'.\ t"
~ ,~-, ":.~ :"' ;
L ", " J
1"'f
Tat ~_Uu irWq 80 4Pah Db" (II.5) t. 00 till rUt ra q\:.y
luft bi'n d~l -81 day OU~,tell tras d51 Tas. cao phep
'b1h d&1 ~ ' 30',Q~ ,Z :
[~ ' pJ = -,~1> '

[SOl.' s6 J = -i ~ + (CT~~)~~~ ,
( S~ 1 ~] = i~ -
(
t) oa/4'. () .it
. ,,~. /o("I"T'
[Q ,1J = -i~ +(~1t7} ()ML'h-Zi~ ~
of oc. / .T '" ;,%- ~
(Q~lt] = i~~ -(?o-Jt)Oc~cp-2i~~~ J
. l ~~
[Z ,t1 = i* ' .
[Z+, ~] = i * .
(II.9)
(11.10 )
(11.11)
(11.12)
(11.13)
(II.14)
(I1.15)
D~ dm quy 1ujt b13n d~1 cua sUu traOong <sat vGi 080
, . II! '
pbep bi'n d01 oon 101 ous d~l SQ, t8 Tin d~ phaang phap
, II 11" ~ .
cae biel1 dbn cara sinh cus »a~k.y. Salam, 1; qua thu dIJVc
ql1Y111ft bifn d~i d~y du eus cae stell truemg 'toan tw dtSl
., ,., ,., . '-
Tc71 080 phep blCn dol tacmg ling v61. cae vi tll ~vaJ:-:
[Mh\) If] = _f 2:h,,1-i(~~v-x~C},\-f(e-o;,lI)~2
r 1 " 1'" /, ~'?<
.
(

)
~;, I
(
t
' ~ I
(
-_
)
1"
1. - - . ~ cr n -x -
2. ~,,-&- ~&- z. ?~" "'if!> 2. ~t) ( 3rz"ft
- i(t}~" CJq~- ~~f~" i5)t'r - i(Q5t~rr>-rr - ~~~II'l)~ +
)
'J .
(
-"V -
)
0
J
rh
+ i (~~v{}.;z. + I t1-~\I~ az, r ~ (JUG)
12
VT",;J=-
{
T(+fC.!n'i-'l!.\T
(
~-L +;;- a_
)]
+ (Ih4 6.)

L , . ~ u~ fIV ~tr :-'£~.:
+i[(it-~"if) +($f)}(),M "'1: (* -7rz)~ -
I
(

1
'i)
J
J
-2: * -'12 '? i. r '
. (11.17)
[T2, 1>1==-{TZ + ~I(-&f.z-'?~)+(iJ~ -~: 7~-
- (~'1 - 7~~)~ +~(~~+7?):z +
+~(*+rr?):z-J 1> ' (II.18)
(
T
3 t1\
J
- f
T
3 \
(
3 - ~ d - 0 '\ .
, T - -t + 2- ~z;&.+ -&a~ -~ ~ -?ailJ+ .
+1 (-e-~
.
~ -v~if)~,M - (&'l).£ of-(-&if)0-
J
At (II.19)
~:Z 3% r .

TIl' kha1 ~r1h: 2-aUIl trutmg
2. 1 0(' !>.
~(Xf-f-,~,'1.,'1.JZ) =2: m!n!pt<J!e: '-8-~? II-IrA.Ie
'".",P. .
- "1-= ~ (11.20)
7C~0l-;-i.?". tzA 'f(P'CJ)[«"-I~faLB'l-,Al(x z)
p "'p At-I tJ {tn,n)! 0(
J[
R 1l.1 '
, lit'! rtl-' /"'Y\
V80 cae quy luii bi~ d~1 d!y du cuB aHu irue-ngt ta thu
dU'Q'c quyluit bien d~1 d!y du CUBtr.img thMhphhi dC'1
vc7i cae phep bign d~1 do! mg. vi dy.t d61 vOl 08c phep
b1i~ d~1 isotopict ie co:
[
T1. 'f.(P'~)[~J(
.
;j ,l (
]
= -1. i1 !L Cp(P"I)[o(~pJL~J\!(X. ~
, (m,,)[a(~l[~ BJx,Z, 2.1 z.rn+1tm+l"",")[CII""l[~"l' ~
(-I)"' !!!
q;(P,q)[Oc«p1C;;.,J(x ) t- LL co~I,CJ-,X:~;Jrft.tli)
+
Z. n+1 tM-t,It+')~l[oc~J'z 2. p+1 1(m,")[0(0( 1(}JIIl (-J.,
(_j)f P Co("",Cf i)(~l[citj11 ~j)m-I+n+<ff ~.~ f;.
+ T . ~ '(\!t,.,)(~)U)J.l (x.:.) + f ."*' I ~ )(
'
x~(P,"-
.

'
.
~(~l(A.l (J',z) +(-~""(n~:(a:.~aI'41-(p-4itJC~l (1(,%}1
rl!J-l, h)(ec JC,PnJ P ".,. '(",,".i)r~1~ 1JI
. . . (rr.21)
[
-2. 1rA'[~(J.;.,J 1 _5-; !!-fD(f",lr*,JfjArll' Z
r , Tj,.,,ft)[C!CcIC, )[fjJ J(r:,z)) - tz ,"",of'(~I/ iJ( pJ(,.J' ' )
.,.i (-I)'"-!L- <f{F"i)(~tM.J
(~,z, +L~ CD(pi-t,lf-of")CitpftJfj.,J-
2 . ft~" rM-I, )[ar J«<,&\l. 2. p+f TCftt,n)««<"'Jf1P"J [x,z)
- (-Of L. (r-I,""1)(cilpJ[~,,1 + "'-HII+~ - ~A.(p,q-~~l
2. q't'l 'f("'.")roCoc J[PAJ(~'~ (-~ '"11(jJ v~m-II~[~~'J(j;~
+(-i)"'~-;" pJ(~)Orfa"r/p-r/1)c,.Jf;,s1J(1(,Z)
}
,
(""n )(~1~.J
(II.22)
~
(
T,,~(P"I)[cit~(.M,J (J<,z)l = -Li(-1f'~(a:)~~a}! (p."
.
'o[~JfjAJ ~z)
. t, """1f-",)e,,,J ~ t /41 .frf:1.'I)-")[~ J[}.A1_-
T i (-1)"Tp("q1( ~),8}~}lC'f(r",-t}[ ,)[jJ (x, Z)
J
.
. (""""")[~J,.1 crr.23)
Nhll1 veo cn CIU1hit b1en d~i tren, ta thSyzoOr8.ng
cae d01 XIiDgthong thCrl. gin. va d'S1 mng trcmg cO lien. hi

vOi. Dhaa JlQ1:each Chtt chi.
,
-' -, ~ '
4 C'.A""t' 'f:hrpt!Vl1'!lal',AI!h",m i;11'rmlr~. hAt ""Pili. "'U$
~r'~v th~J'th ph'» hOD~ ana (fa tuyh :If. ~:xet ham
!tal entea ch; a1~u tru.o g.
<0 t P( )(/~"Z) ~C1,'t' 1 ~) 10:>
.' ,.~ , ,.
tror~ (10 €-;7 .'1., "> Is cae toa .~ sp1Da BajOftDa Ya Dt cae
bi~u di~!1 vcn deh 'trung ti1lab')sng o. ~ gl.a ibilt
bat b1(a
cuB vacnuua. 108 cO hi t1u;c sa" 461 vb1 ball ba1 411. ou1
sUu 'tmGDal
14
. ,
<ol1>(~,~,'l)P(y,t"5)lo) =
(ot +f(~-i~,."e- -i:~JI"'l) ,(+-'t),Ct- ~y~(y,o.o)J~" (; ":-)
PhuoJag trlu (11.24) db ifa ,hll'aDg U:bIa R 461
" , ,
Ted cac t1'W'Ag thUhplah:
/.
\ ~ ~ 1 i«t ~". -nfJ. ~ (pr"',~). (.)
,-O ~ k- 1ft!Pi!
P
!a! ~ c.
I {; «,.l[ft
,
'.'
.
3") x

y- ,;<If:" "'~ "-r j
-tl -~ -'.( rr~ ~(F,.~) (X")/O/ =
~"" ~ 'l '(~'.""fJr~"h,~J.
(01t i -f(~~fr~~ 'l~'lV')+ ~tt<i~~Ci~-rr~~f4t-
-tf< ~1}.~ a'" + V~~JI" )3 + ~;;Wi.,tt;r" + ?y~'{JfiJ J .
.::,.
. ~ 1-( ;-'1- ~'~) (~-ff{,."')(2Jtz~!')"., (ifA ?;A.),
L- tft!,,! .
""":0 - eII. ~.5) .
fc(",,/J) 'P (0,0' . >
'(GC, ee l(j\""nl(X) ()f.'} \0, .
~\>- A ~- A <!1
1
-
h
.'"
.aaag cach can UIUlg b, 80 hvO'Ccua oIlY t UBkhu
nhau cas cac t98 G9 spinata tbR dl19"=cae h~,th1iC' g;1i1s eic
"'",,', ~
(
ham t~ quan ha1 c!1~11cua cae ~ thanh p~.o v- d~
khao sat oae luy thDa bio 2 ta th~ dlfllc cac hi - tb.:c 'eau f
<i'.(.l'\f'~(1C'»1- i: ~:<F(x)A(JC') -+ !(ys)! <cr('J()A( "ip-
-i i (1"IYst <A}I(J()Aex?) -f ("4)~<A(,,,A("'1>: 0.1 (n.26)
15
(II.2'O
<A';.«C)A('~x'.» +f ~<F(zt,,)A(~,~ -t-i:(~5't<O{~~fY~$' .
-i (/ffMts-t<A:;~x)A(~))-~ ((~l")x )~A(x)A(x~~; (II.28)
ill(
< A

(~) 'f~'~ (x') > = -< 'f';'(X) A()C')> ,
< A(x),:(":")> = < r:()()A(x'» ,
<A{x)6(JI.') = <.&(x)A(x'» ,
<A(x)~(xf» = <~(x')A(x/) ,
< A(~) F(2.lx'v ::;< f(:Lrx) A(~» )
<~(~) (/1",» = < Gal,,) A(x,>/ 1
(A(x) A~)(x/i'; = < 1:1.,::) A ()v) I
(
"\1.0. A(I), / (I) ') '
<
"IJI)
A
~
l.t{~);S(X?I= -\,4\~(~t(,,91 ::- . "r8lp(;c) ()(1);,
1:rcmgdo 'ta 'dB.Jri hifu:
eofc,o) :: A (K)
- J (J'.)
,
co(1,0)-
10(. ("1.) :: "f 0( (]C.) I
(II.29)
(II.)O)
(II .)1)
(n .)2)
(II.')
(II.)4)
(II.)5)
<p~;:= it;., fi,,1+4. (\c1p 6(~1 + i(~c~p "; 1»,
16
(0,.) (I)

t (,,) :: A0'(%)
J
'f(:"" =1.!- (f',
~~CX) - .~p ()()
,
(0(0/2.) - J
c
f
(2-) L
(
~ (:., . ~
(
f" ,' -'\ ~(:')
T
(
X
)
:: 2. out (](,) -r, ~CApJ:i
(
~) 4-1: 'j Jy"-J -'~0c).
!:IC~ y - Cl'r e< I
Cae h~ th.:c ma ta thu c!ll9'Ctrons tieu ~c I1~Y cO .,
ngbla hinh h9C 1"0.rang: Cluing Is bf qua c~ bitt 'QuiD. tIs!!
tieD troDg !lieu. khong glan.ar, -r~D.g.
Ct:!lmrta' TIT.
A
3nu XHONG GUN HARaDXIC
S1eu. tnrCong me dt.nh trcZ1g Bien 1chong gf.:.aJJ(II.4)
, Jl."'. .1.
}O nhuvc diem la ch.1la que nhUu thanh phJl::! :Ch;a1 trieD (theo

, - '." .b -i. .
}SC lay ~tla cua oae tQ8 c!Q spinO' vO(~ I -e-~ Va co MIln
thanh phb spin cao th i:ta. i)~ IDat~ cao hypermultlplrt TV!
superspin va superiaospin thgp. c~ ph!! ~~t c~c d1'11 k1~JJ
hil11 chEl len cae sieu tlVong <!~~o~l cae th~ ph~ th~.Tuy
nhien, vl~e 9~ d~g c4c stell t~g kem theo cae di~u ki~n
h~ eM nha v~y sa lam mSt t{nh chat sang sUa hlnh hQC eu:
cue hlnh th.zc lu~n stell trl1Ong. kho khan trnng vl(C" my .
d!;Clg cae Lagrangiu tlZO'ngtac :,at bien, n~ien cUu 1; thuy~t
nhi~u io~ hi~p big!l v.v
Jo do dol v~ 81eu dol x.mg mD r~!'lg SU(Z) cIA co
hkh th.zc lu~ s1eu tnrcllg sac cl:c. 1I19"t~t. kh6ng kell! thee
~:.~u kl~n h~n chat ~t kbac. co Ll1ai trl~n thau ph~n <lu ~
~~ ttlang .lng vO1. cae hyper!!W.ltiplet thgp. C~c tae g1a Galper-
in. Ogtevetxk1 ya cae cQl1g all da za.y dlplg thSnh CCLg hhh
thuc luij.n steu trWng d~t dUlle cae yea c~u cl11.lvb nhe, dua
" ' A A , . ,A
t
. .
Tao ~a1 D1~m 81eu khong glan ha!"mcmlc v~ Sloell rt:O'Dg gie.i
doh.
1"7
, ' '" , "'I 'I; w ~II u.~'I!a"": .9
1 "'foIchl. e1! ~ ':""~,II'jC\!,"" va 1: "ft ,~: ru dl:U4 cua
vi,f'c.t.lnt';l£ifl:l,siu kb6Dg paD con 1tb1 46i vat ceo phep b1h
de:1rie:.t' ;:~.Lnng JT. '2 : h'JII (II ) 18 khao Bat neat
kb6ng pem .
, "1.~ ' ~:,-+i;e.2. 1 -&1 ; i~ 1 .
(IIi.')
cacsieu i~ nonS slea. Bhang g1an con nb 00

'1d1a1f:r1~n,~h 'Phh ~. hone ~rahUn. hlnh tbac 1uIa
81h :: ~g dUng ca 8~ DB)' kheng cO dnh hi~p
bitn StJ(2} .
case. (XU.1) chi thiza !1l'>indlS1 xUng trong 0(2) (hey U(1) }.
1'~~g vTt81e.u. kbang glen harmonic ls: dUng mOt 8ieu
.'." .
&Sng g1aJ1' COIl t~ tf (:rn.2). d~ng then. dim V80 bien so
'" a
d~c'btft mc1i d~trlnh bsJ' 1i thuy't dLrcY1dQIlgbi~p bi4n
sri(2). Caa bilin so a:1i.phsi lien hi cac bi~\1 di~n U(1)
vM c8eb1~1i. dien o~ sr;(2); 40 ls cae tQa d~ harsonic
~g,~t.chl 80: ~ <1: ~!ij6 St;{2), j: : chI s8 U{1)). cae
t~~ d§ bar.onio laeac YO'huang Loren Va 18 cae y~u 'to' ch~n
'.,. . Sf! "' it '" . , 1 J(
.cue u.i,8~ ~-~msn~ ,/,U.JO'cacbien so harulOn:!.c, 00 the cbuyen
tu. b1~1t !'",Ii SU(2) thaxm bdu di~n U(1):
'\f+:i;1f~!"'f, 'f'- = 'Yi u;
."
Va DgII9'C 1011" .
-t
"f' = 1.4+1'\f- -u-"f' .
# , ~ , f~. . . +
3a~ do ~3cg1a trJ.nh Day cae tJ.nn ehft cue 111 ,quy
t'c 'V'lphb. t {oh pi18n t'heo u.
.,

, tLeh"- , { .
2 ~ BO'J!'i~1 VB Bien t:rvenw mAt t ~H CO'sa
gi81t:lCh.l8 cO'.a bao g'Omcae t9a d9:
j ,. -of- -+" - :t

}
l'x.a 1 -&~ 1 -&~ ' -&~ ,1t~ -' Uj "
en!.2)
- -
18
<
,
~I r /It. . M ,
(
i '
)
~ -
"" = )(r - 2.r uri»J. lAc,L$j) ,
Q 1;:=' -e-fut. ,
-v~ f
-+ - ~
~- = '6:.u. .
-,-V 0(.'
. Stillkbang glen con Ten cac tQ& d~:
S /4 .+ - +l
l )(A ' ~CII. ' it:, U -J (III.J)
ribg nO 1& k!n dol Wi cac pb.p M;n do1 s1e\l d51 Ding Sa",
.
va ct. got 1& slell ihOnggiaD can gistt{ch.
31h ~1UOna :zac dtnh trone; 81 en kh3ng g:t8lt cen gi81
-t{ch d!lllC sgl 18 siill ~mOoag g:tal tich: '
~ J; tlf' + -+'" ~ (i)
~ = ':t (x ,-& 1" , U-) :: .:t.(ZA'U)' (III.4)
SUa. 1;mdng g:t:l t:Cch (III.4) khan~ P:-;9thu;c -a-, t';.
.

va 1101chan.s ~ DUIg "t!ci1 1](1) Is. q. S1en tro~ g181 t[ch
cO 1d1e! ~rJ.ln th4nh phh nha sau I
~('f) FCII' ~ '\U(q t) -'1-~-('i-"
]! (~/LI) = (XA,u) + ~ TO(("p. 1"') ~ t7Ot'1 ("A.IA' T
( +-&'1-)N\(4'?,, ,LI) + (i"'~+)N(1-2}~.Ll1+( e+!T"".&'"f\;:r-~KA,~I) -t
(-e-"t.+)-ft+"'.1.(4-1)"

'\ +
(
i+.e:+'-a."!';;"(1-3) -
:;;Ho- \~,IAJ / ~ ("AI") +
(iJ+-e f") ( i't-~+) 3>(4t"'4t'St./ 14) .
(III.5)
, a-
cae truong tts8Dh puan trong khat trien(III.5) pi}\1
thl1~. 118)41 cac ~a 4~ khOu& thOotg!sn xA' C~)J1vea cac t9a
d~ h8Z"1lOG1cuf at tballli phln de} 101 co khat tr1~n th~o
cac t9s d~ harmnic, v!. dv. dot vO1 P{q)c.XA' uZ): -
()
00 ,
'P q
L
(i 'ft"'" \ J ) + . :1- - -
(
~
)
. .f );; U. 1.1. ~
J
' Ll
J

' . (III.6)
%",1&"'::0 (~) '1". ("f"'f.1 n
. cac t~ feil'" 1n'tq ;11 ;}n)(xA) cbl conphv.
-to %" va 18 Me 11111.1d1;. bit kit. QI.1Yl1oan toM .do1
1!
:mng cuaSU(2) wi isosp1n.n + q/2. Bhl! Tir, m§i; 8~~U tmODg
gia:t t!cb.ch~ Tah~ 1.soeptn. ~ Dhlen t;mag tbfc t.; chi
~iil 1$1 c~ 18OS'pU1~~ Dhlit, cac 18ospm cOn 41 ~ o8c
~ . '/, ,
~c tv do b6 ~rv ho"c C8Cbjc t\1' do sause.
,
.3 Mq~ ca~ t/.'We~.muJt1-nlet c~ !d~1il d&i. ~r"2 ~"'g
si€cu t=~~ gi~i t!ch: H7Pft1IIIlltip1et 7~U8
chUB 1aoftoublet TQ huOng 'fi 1.eosingletsp1,na D1rao
( if'<'>.! .S~) tren TO kbOiluvng. S1.eu 'tzvGong gLS1 'ttcb 'turJJl&
~. 188ii!u tmo.ng giai tfcb pbac cO tfen Den 18. + 'I :
q+ (ZA ' ui) .Hyperuw:tiplat Ho S1;ell-~8D4 cba
iaos1:nglet vobucmgj', iaotrtplet vo buC7ng ;(1.3) va
iaoa:1nglet spiDO' 'leyl -then vo kh51. larzng. lith trag
gi;1 tlc'h :tacmg aing J1 sieu. nvOng giSt t{ch thvoc cO t:lab
;(1) b~ng 0: (.I.J(ZA,t#) S1.en t~ g1al t{oh v *CZA-U %)
, , .~ ." Ie
tU'O'llg mg vCri hypermult:1plet trm:m;g c:huan chiIa :l.8os1.Dg1et
vo huang ph~c C, 1aodou'b1et ap1na .jo~ X va 1aos1Aglet
'-~ctC' Tjt'\ . T1rC'ng Ung v-71 Ii thu7ft cfldn thOng th.a7ng.
V++(z.A.~ u:t) dU'~ ch9D- 14 thl;c.
C
' ~ ' .'" , h -t ), i "i. .
4 ,",eh~ than P"!I~Acec, aJII I~~, ~n R ~ CoB
t ~ vi . i -!ch

C
'
s1
A
t

, . rllO'1'l~ iron;:! si~n tracm{l II ". '. : SC ell mcmg
gi~1' t {cbkhorg ~ rant; btt~ bO1. cae cn'l1 k1~n I1p ch')'do
'"" '.' . , II .'."
do do1 VO'l.cb !.mg. ta co the ap d\.U1gphucmg phsp noll 0' my.c 4
, ~ '- ,
chU'O'tlg II dol vo1. Bien tra<mg tong quat de say eee hf thVo
giue cae ham tu.O'Ilg quaD hai d1~m caS cae trilOng 'lihSnb phBn.
vGi cae bype-rmult1plet 'liren TO kbOi11lQ'!1g., JIbe, phllO'Ilg 'trbm
~ jl.
b1
~ ",,' '.
CllUYEndvng, ts cothe en dien caetruangbO t2V qua -vt
se ttJong Ian eae txuang 'Vit 1;.
, A' . ,
DUag phaoong phap J1h:r 'Y§-Y,tac gta da thu duvc cae
hi th~c.au g(1ia cae ham t~ qaa.Dhat dll. eua cac tm~
tron~ oaeb7P8r~ltiplet. vI d¥.'doiTO1 hypermultlplet
1'8,.81; - ,SO!m1U8:
20
< Cf~x)'Y(x'» =-< 'fcJ(}f~j(') ,
<<piC") )'(Jt/) = -( frJ("f:(X'» ,
<1f'(,c,~ fcX/)>= <~(x,) ~ ~(~) ~
(~\~~<'f(~) 1f1x'» = -<.~(X) 'f;(~I» ~
(Ill.'

(III.c
(III.9
<
. k k i'
. 'f(J() Ap,('!.lj) :: <~(J" '1'e](')
{III.1(
,
k .'. . (III."
( ~(.,.) :;: 2.i~Cf~x) tren vo Ichc1 luvng)
Va do1 v6t hyperlllUlt1ple-t Howe-Stell-To1msend:
,. (CfC)()'tI",)} = -<'f~"() fC)('» ,
<
~.P k,
<
It th(i';) ,
. T (x)t;(~!}/=- "'(X); ~(',e)/-'
<.(X)~i (X'» = -<'fi(x) 'r(x'}") ,
<
Cij} - ~
<
- ,.b(ij)
<t> (~} 'fk.(X")/:- 'f'k(J() ~ (".')
(III. L;
(III.1J:
(UI.14)
,
(III.1S)
<
$( -,$ .
(a;. )Ot~ 'f'(IC)~ (Jr') > ~ 0

.
(III.16)
"" "7.\
ceo hi thUc tbl1 dtJl1C co Y !Jghu rnnn h9C dan gian:
DO 1.4 hi qu8 cua bS:t bioen tInh Uen trong SiEhl Ichang g1.an .
COla 81a1 t{dl.
21
Ch~ IV.
."
HIP JiIKN ~PO.B.ii4L TA StlP:u.CQ.NFt'>~
cui CACaO B!JII !mtOllG
1
" ~ "'.ft . ~ hiSft l"""~
Khai~i~m VA 1;~en eblNai hi~n coni'orme.: aua1
miJr. hi:p bien conformal 1.8 811 rJJ 1"9ng cuA 1chai D1fm h1~p
bien tllang d01. hong 'tieu aye ~ tac gib :1hzc l~i dp:h
ngbta U~u muLL hifp bien confo:ral cua Ii tbu,ft
'truOng, c4* -n liVft cae 11 tbuyit ~ tM. m&nole Ueu
cbuLa 'ria.
& SIt. .~'"
2 ~,p 4;;huan Mfn bip~~to-rft~h _t cae li
- "" """ ."", eo
1
III-
tl1uyet co do1 .:qmg cao ban: ~o~ ~ sl1perco uorma. cvng
t1~u ~c Uy t~~ gt8 Mil vA cb.~ bin ~nb d' 8811: BI~t
La!Xang1an 1; 31eu d81 .:x~ ~ dbns then bi~p bi6n confor""
mal, th! 1; thuyet 18 doi xt1h~ 811perconfor~l. ~(, ~~ d~
. . .'
Tite nEu, ta cO the tlm vI d, c*c mOblnh co dSl '%ling

superconfor_l~ng 'c&cb cham! ~ ~. 11 tbu1gt 8ie~ do1
~ co ~t bien conformal, bo,e co the- %&1 d~g ~'c Ii
thu,it c; dol Xdng 8~c~ormal ~ eAch xuat pbat tu cae
LeP'Bmghm )UtI> bien con:fQr_l, U dJ -'ChelAV$O ~c tia~g
hEmb (pa-""tner) stell 461 %ting Te %81 d~g 8u1 1"Ofigs1.4!11d61
:mng cu~ 1; t1:uyet. DOJ1. ph~ p)Jip d~c ~. tron~ ib.1
0' d~g e&c ~6 hlDh super~or 1 cad Abl9Vt ~bnb8V
. . .
Va cua taegia (um ~UO'.n,£ V).
3 !~t s.q 'Y! ~~~ng uiu ~c nli, t'c gi. d~ .\0
afDb Q ch~g lCin)la tri» ~ kh4o sst 't!nh chit do1 ~g
- "upereo:rl"ort:al cuB JIO hl~ 'Yo h~g ~lral 81ei;,dS1' ~!"g
~.i tv tlrcm~ tac ss3 a 80 h~ d~tn d§~ lvc sHud6-L-
D.ag 'CD ~8-ZU.iftn.
22
Ch~. y.
. . ,. 6.""'"
C~Cat:) aDZE LY mu"d'! r:u.;v.a ;XJOOl _rle;
conoRJUL VASti"PEiiCOJFORJULAI PHi 1fJ -rr: PHd
. .
DO! Ding oontorllel .a .teu <161~g ct_ J ~c dol
%ling thi h1fl1
; nitng 11JQngr't cao. vi Y~:r, t1b1h01 phi!
CQ coo che pha ~~ c&c d01 ~ na, C<1chi P~1I3yo. dlJ"'!e ch~
y den nh1lu Mat h:!.~nnay d01 Yat e;e 151 mn6~Y Is e<7
,. . - '.' ' - I J
1
che phs va t~ phat ~a tun 1;,1 cae ngbl~m c~ 1ien 0,1
, "
1Astanton Qua phllC1ng trinh tr\rong.

1
'IF , - "' "
'a1 tro cas vacuum k:hon~ bat b1.en t1'Qng cae 11
~'_ ,;;.,. ,,;;- '".< :'~ "'-,-~",- -c'.
S
"p"
rc
""
n
"'
or
-"'
,
'
,
" TJ:.
t
Inn
,

~ J~' ~~, -""'" ., ,~- '~ ~ - -' ~, -« " .,
1y thllyet t:I"\ldng YO bU'l7ng -r co i.a~7:;".l::?i::!cl':'- ~~:::>:d'Jr'YJl
trong khang-thO1. g1.!m DehUIl. G1& s~ gia ttifcY 'Y9ng VflCCIUI
"
t
", ," "
kh
-
b
" ' 1t." t!"

Qua can tll tr,gt:1.ngichac, ong v~ ang ~vt hall! e-gQ Cas t98
lip khans thO{-"gianl
'/,.,1 0('1.) jO"" ::: i!)
, ~iI;)
"~ I ,,/ I.
{I.].)
Has 1(%) th~a p)1ugagtrip I4grar.t.g~ igJ J"t;~~
do t~uOng!chOngPM1 1a to'~ t.; - nm ~I:f n.;~ ~r~cA
ddn.
G1&sir Y&eIlu8 !~) \f1ong 1)1:*bl'n cohtorm41 Cb!
~t bien I!S1 v.~ nhom con ~'o 11&~~ hbQ~ ~0111"9r_i# Jrt~t
, '
r
'" .i. ', ",I'
each r~t t'l nhUJ;\. nguC1. ta ngh d~~n'icd~g ~911 Po~~
l~ nhom con bIt bien Cll~ va call1l. 'ruyJ;h!en. dU", ~1 ~
dsta ,-, .1!>d>c ,
<OiL'P(;K);J?4\1Io'=lax,M:;O 1 ,(1'.2)
t~c ~c. const. cae t]."Wlg bin)! ~aCQU1I10',1 It\ng a~ MP' Yil
Jd18ng daa th~1I net gl md1 vso 11 thulft. '1IIJ1i!chac. trong
bAa Db., cac 11 th'113t t:ruang con1"ormal !chong t!m tI!00ng
~cs qI18D:taD, ngbi,im h~ng so cua phU(tngtrlnhLagranga-
8Gler ~6 411. kh8ng 1:&. 1:01.
23
'1 1;~g hay cue Fub1tt1 lei dUng lam Mom QOn b(t
. ~ . ., , " ,
bH~noua, vacuum 1:a khong cbQn Mom Po1ncar~ ma Ch.9n Dhom
"
deS1tter sinh bC11 V'1 1011'Jt,.AA)) va
1 1, '

Rf' .2(a Pp + -;- X!" )
(a Ie b1lng s6 cO tbu uguyen d§ dei).
Dnu k1fn bat 'bien RJI" c~ vacuum din dgn ph~g
1orinh.
(olrcf>~)I~JJ~/=~ ~ ~~~%,f?dxf'tJ)~)} fL (V.4)
eV.)
=0
" , "
(
Wgh1~md~ng 1;hO1.cue pbacmg trJ.Dh (V.2) va .tV.4)
tan t~1 v~ co, nhfmg d~c d1~X!lrat kh3ng tBm t.ht#lngl (1)ch mg
tl1'C'I!g.tng T<71nhimg ofu blnh t~ dput ~ th~6.cS '1418n8
gian va ~a then. g1an U.nstenton) , (u)b giG:l hp bIng 86
tU'O'Ilg tac 1>6 cpc IV °C1/g) v~ trong thaitrdn <p c 'Pc + ;;'
co phAn dong gOp lUn cue cpC, cc>ntrnOong da dtch CP" b1~u
ditn nhTmgth~ng g1angluvngt.1o bt3. O~o nghi~m 1nstanton
{bey giahpt) cuB cac phllO'ngtriM t~g Eilcl:la'e b1~n d~
dll?c rat nhnu ngu&! quan taIL yi chUng lien quaD de1',tv!Ji d'
c8u trl1o ?BCUumc~ If tbuy~t, chu~ Yapg;-~g;J,.Sf'J;I1~n nay co
rilinu chi da.n cho th8Y ~u true,: :nt.cmum,cu~, 11, tpuyet ,Y~, -
~ll- :La 1'«1; ph:rc tQ.P,,'" .
2 £Q bin!; codQ'1 ~g su})eroonformal b1 p1!a :&1011
nhtr cac 1nptan~cn:Aku.lov va pa£ihnhev 4'ii ~y d~.
kheo -at m5 blnb 8uperconfo%'1D91trcng Bien khClngtian (1,2).
lito r3lnh.c%o1.8 ~sl1yr~ slen ',46,1 xU-;I'lltcue J:Yj"t;tn:ygt
~ 1 _no bit ~1. 'Conf'orma.l«::<1h~e l~ t~ .blt ,i
. .'
bien oo~or_l) cua .&J1aro- hM.;'t':' Pul."
24
,'.

»1 co 110,hinh IIIU1g~,c bvng caS 11 thuyet t~
~ tac~ c!.!!It~o !tDh4t 1 chilathong g1an n~. hong ulu
Dif}~ni7 tlc g1s bin 1. ~ trlnh C&,.vl~c BY dqz:g m6 . ",
}j~~n 11 t}1Llyit,tru&ng tro1!g slea 1dtOngg1a~ (2.2) co l!o1
,~~$ 8V.pt).rcon!ormal bt- phfi * tl1 phat nno. cac 1l1Btanton.
Xu.$t t>b'~ d~~111cua 1o'c 81& l~ Iagrsn~8D ~t; bien. cozU"orma1
o~~t tr~ TO h~ th~ '~1el1 0 tron'J Ichon~ thO1. g1an
~Q1tdQ bal, cblaul
:;e ~ t(~'f)z. - tupC-~'f) '0
eV.5)
r.~gian (V,,5) 11. S\! t~ tll ba1 chi,. cua
'" ' ,'.~" ., , ,- , ',' , ' ""
~~~ai). (!~ Spa1;1;1i tuy dUn s3 h4l1g dQng nJng hong
~ 'hgp he1 cbn~ cua <iuiD, te CO d9-Ug quen dlmg han
(~0!16 b'U~,g h9P Chi'. Spas~ P.1 -dkg difn"cite <lIlO
- he. cip"'Qai). li$hl~1IIc~ .,dD cua' phliCm'!;trhm tralmg the).
.<111a 1$1iD-bc!t bl~ de Sithr CO dong:
cp,c .2
,
' In
{
',Il. ' a2 x2{
,()() g f ~ 28 J' .
(V.~) l~ ~1~m c~ d1~1'J,lo~l instanton cwi mehtun trutmg
(V.s). @&. Mt blln o~ nghiem lEi nhbm 00). 3uy rQngsiEiu
451 ~~e '(V.S> cbo t~ Iagr~g1anl
0".6)
~ :: i:(~CP)~-t~p(-~'f)+&'P~ty-l{f I2J(p(-~'f)(lfo/},(V~1)
$6 ,t$ bi ~ base 'fv~ t~g ferm1 ~ tll'ClIlg tac vGi
-, ,'~

$.~ ~ Coach steu diri nm$.
., " " .
1
3 QA"th"n~ ~An, ~~2 ~~f lic} h Db -my d1plg nba
trb eo d61 xUngsuperconformal b1. phs va til ph~t nha
~iiS instantO1J (V.6). Trong t1~u QlVcnay. tee g!a ld1ao
s.t orl.fide t!Db cu$ 1; thuylt ~ pha phs va tv phet dol

~.
2S