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

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a BC p~ BOC.TRtING~HQCCEUIENNGHIEPVA D~ NGIm mtfdNGB6I HOC TONGBOP m-AMIm6 BDad ETh'E -===================================~==========

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If~1n 11690Glao - Giao 811I. PhO.tUn sl.

DucmgTan P1d - G18.o all It TUn .1.

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Ng\fO'i nhen xet 11

u~

,~en xet as

, CO' qUBn nhen xet,

. bao vi

tid gOi d:~ng chlIm 1$

, .. .8n Nha

h9c ~Ang h9$>T.P. JIb - Chi -J4iI1h

,," L$ an se ~ n..mc hW t(l1 ~ vao hbi

¥ nga;y

thq

nibn 1989

Co 121' t1m hiAu lu'n

an tCl-i !lhll vien 'lrIICIng d:~ h9c

phS gb Ch! I[~

va t~

']hit vi~n Q~c

Tang hC1.P~~ 'gia.

. a

.

khcug ihc,i glan can ~n nhat Qua 1;

lincm doi ~

tI'lZCmgluvng t& tU'C'ngdot

t{nh la nhoa Poincare"

ly cho rlng

.Doi khong ..

, ..

xu§:t phat ly thuygt

, la dang nhEt va d~

t~ quan ni~m v~t ", tuong do1 hiP e~h~

fIij fJlu

thUY6t me; Poincare . cua gian thai vb vi hll6ng, tbay khi d~l lfuo~ P01ncace

co 10 tham so,

tu. 4 - xung l~g

..

Pp.va 4-j;enXO'1110men xung luvng ~;"V. '.. ,.." Ie Mom d01 Dmg ch~a Mom ioincare

Nhom conformal

"..

,

~

-

nhu mQt Mom con. h"homconformal "'" vi ", C9J1 co vi

ill cua no bao gam 10 vi tll D wong

la nhom co 15 tham 80, cac tll cua MOil. poincare V8 ngoa1 ra , d01 co den tO8 d9 T8

"".. ung vc11. phep bien

cae d~c trtmg lll9'llg t~ khong dU?c tlnh ti~ bo~c quay h~ t9a dQ ichong then. gia.'1. .. ..""........ cae vi t~ Qua no la ceo tOaD

c, neng luvng cao d~c

ido. r§ng

nhom d01

ntng

Poincare

b~ng

~ch

d\l8

VEtO

boae

'Sieu dO't Ding ket h9'(>cae truang ......

xung va do do .dan den

tb6ng i:1hSt c.ac:

'..

""- eO' bBn. cae

, traong

ly tbuySt

.~~iu

t,

Ji,

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cac ph.p bign dAt doi xttng 'Ych cac tham 85 spinO' dan den Me):; sieu dot x~g. ..,~"",.. .. Va ferIti vao cung mpt da tuyen dot MUng khe Dang to ldn d~ xay dlJng ly thuy't , cua cae b,t tllO'ng tee d6i ximg co mpt as t:!Dh chat 1; so vGi cae l;tbuygt , ~t beng 80 ta1

phep blin die trllllg. d~1 conformal ~t .nhSt g1lt bi en hinh Is nhom r~ ~t Nhoc non anh sang.. cac thlJc KjA tlJ\;1ng ling vai conformal bien conformal G:i.~ thUt ngb1~m :tEh1 Xf hptolD-had1"Onpbi

.. db vong

.~ tat

. vacuum tr1~t

tbUI SO'phin Q g1~11 1'0 rit kbong siiudO't %ling tm:m.g ang, ob J- . ca cae gian ~ %Un« dS1

dhuan hoa h~, t1eu, trung binh Tacuum CU~ tenxa n!ng

luvng tr1ft tieQ v.v HIe ~Iu cae 1i tbuyft 81~u

J

1;12,,",D&b1,.

chaing II:i.Dh.Uu.~S1

A-~a1-C1.i'-'~,'t rO r~g

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v".4'11 Jf;Q-ch* c&. Tlj,.g . . ,.

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s1iu 461 x.ing ta 161 thc1a' - 'th,. chi

th5ug Dbgt ~wng taer' Steu d~1.g'

si' BP dit

-1:\1.0

m§t do trons ph~ hOt, bOb chI ad t12ams6 tdl y cqA co tb~ .~~~ quy3t

tbSD8 Dhlt,-s1&u d61 ~g

thuy't

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cft h1e:tuc07 unU"1c:atj.on)-, V.V..

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~Dibg~ Db1'~. ~S ohq quA1;121101. qlq giG gh 4'~Dh'~ DUt't h1,D r~h ~1't1 cgng trbh 11 thl1ye1: Db'. 11&. hf .1,~o dd1 =g Ilguds. ta olio rh8' h1fn 11&~Ii dU1 Db(t - cbo mic v~ d'a' J18l1gt4J. aliA 11 tbu1it trft 04C 1; dUVc kIlla oph ~ thuft' Qua vh 'boD« Db't thu1'1: 1inttyet1:12&Dg.«, (supergraY1'ty), ... thee y t,aoDg 81@a dQ1%Qbg;

sUI1 day Csuperatring) "flu d\P1C ":~Id1ai diu

Dbol\401 ~g .; . 4:8 d1 8a11DgbUn o.

.-. cae, ~~t qa&'.h

c&c r~, n01 trill. Saa etay '1. w.t#.~ cae v~ -' 81h

c~ tl<; ~~I. gtp V$

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tao gt8. tha 4Il11Ooio It'

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phb o. tt'O11g 818u c!~1 x.mg rJJDrQ11gsu (2). %81818.11tratmg If . 2 tAng quit, 't1'pS 461 =s tUQ'Ag!paD_t bvo.s. ..

tb$mr pItIia.trong sUa. '.

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th41 ftOU\l1l 1141 b1ea tbuy't vG1 gta r~ng. 81~ hlJa

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blim thvc lup t:Ccb cu8 nm)1Iitac gi8 (;olperin. Ogievet-

thu;ret

Chi nb't

sleu dol xUng';'

JIbe, hlnb tbde

cac li trong SU(2).

lufn ~;rtcac

kboag bt

cU: 2 chzqe 110 1;. bO1. cac

~Qc d01

t:Coh - cie 8ieu truang tU1 klin hincbe cO t:Cnh ch!t tr~g'

rUg ap dlt. Do do.' phuong

co tb'

gial

ticb. tAng

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l1'n ltet qua,

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s1eu dO1. JJ.

8P dpg ihac ~ diem cua cae t1'llC111gthaw pbb. ",.. tbllC g1ils eae he. cae 'bi

pbap hi cic beB! tac J tvcmg quaa.ba1. cHell

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thanb p.bln trOl1g .cae h)'perDlIUplet

J'a;ret-

.Uu xk1 vA cOns 8¥ - blM tbiic lufn c!1tVCtbw nhin 18 raOta day-c r§.t:g dl1 a~ "'~cblt Ii ;; 2 cbUa 481=g bn>ermul'tiplet s1€u tralmg bb1 cae di'u vcn eac sUu Jibu steu tm~g. tllO'ng quan h.l gt'8 tbu d. cue. cae t~ Sohn1us va Howe-Stell

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if;

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,_if _t

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th@h dol

:dng rOng h(l1UDot =g sau v\

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hvp dQ1 DDg conformal TO1. sUu superconforllBl. hl~p cbu~ tiell v~ do! Ding, slell le.ld~i Dng tbllyet; tae d..nh aO hl.nh TO hu6ng

doi mg ~~c ~; neu V$ cllling m:LDh minh d\ bien' 8llperconforml: dang superconformal. bS:t bleD conformal sih l~c sielld01 xttng cuB 188S. Zumino. %"

Hlu 119.t Lagrangian tbl thC1. le. b1~p 1:d..~ conforl!lal DUng 1.. gi8 xet 1; v{ 41\1II1Dh b9a, cua va superconformal deft :.Ding vcn tv tllO!lg ,tee gs3 .va 88 h1nh dieD dOng

.,

.1-,-""" a" .. cua cae 11 thu1et - De t1111h1el1 cae die .'-, ,.. ~ .. trao-'Ig bt pba Ta tv phtd, :nmg eonforll81

trag co dol nmg 8uperconformal

siell khanggian

b+:t

l.nstanton

"... co dol tee 818 .i d' xuSt va kb~o Bat 1110binh 11 tbll1't trong (2,2) pba va t~ pilat nhc, t~D tf1 nghl~1tt c~ c:l~n lo~i t;~ pJt~

6.pha

t~g.-

tthl~

r"s va tv phat d61 Ding, 80

:;

hnn va 8&q1.r83formal ' '..

:tera1ont\tcmgtaa .. D'tiauaft c ~s~u

trong .~

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11

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hUb. .~ ta cae fhlDs c1Gs 1IIfIt8to"& aO1;~ aOt ~ miDg. Ph1lCmgtrlm ~t~1Q11 cua boeQl1 CAP D8h1faa ch~ cua :tera1on.

,

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.. qua cua tae gia

" 5 ba1

Ita. dktgc c&ng b8 trong

.Ji",

"Czechoslovak ...

of P1Q-jics",

"~eng

baa ihoa h9C Dp h9C tADg hClP danh JII.\1Ccae c6ng trlrm

theo 4A t8.1 1$

an 0, eu8i ban tan tit

bao tran cae t8P Chi. o"Terpchi T!t Journal ~8nh ph611& Chi 14inh" (xem b~ GOngb8 cua-tae gi; " ntV).

Ban 1*

an, Dgo81phh .& ~u va k't 1utn, CO5

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t

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tat

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+

+

+

6

xac 9'a tIlc1Dg \fIIg

«

,

mfOjt001 D}.riG, POINCJJiE

n'clc

ilf R~rm dA 1;0

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;fJJ\

Ch~g ~ mane die trlln~ uhf!' mon V$O 11nh"vc

I Cb~g ~,

\Fa cae ',1DC1rfmg

clla no I 1110111

ne,b1& c~ trong &) ~~ Sia tr-lnh ~y cae kiln thuc v~ t:b&I d8r ~ Poincare con:f'o.rmel. %thom81311 d6i Ding vA nh~tn auperoonfor~81. .

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t <>ngquat P 1a Mom

lbomPoincare

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pbep

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qUt

b1Sn

d~l

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Loren uSn 4- *98 dQ. Ibom Po1Acue

t6ng htPP~ ..61. ~etl\.

la 1

eua lith uygt

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tit . clol

tllO'ng dot phatb1E!11Mil 8au: thai treng

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bien cfAl thee bl~u c1dn

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.,. Pi"

la Dboll 10 them eS,

~,\, 1e Yecta tbh Jabomcon cui P @1I ~e phep bi en d~1 (1.1) va ~~1. 1h,6Ephil Vf1l n8ng cue MOlD Po1Jtcare u.~o' T:i.en ~ bS::t bib # tLlO'!lgdQi tum d. v.cta Po~nca" ., ~..' u~ 1;a Uh Vi

t,c t~ 1i. 4 vi

Ci>" cue ahOmcJo. ta tb;m tUn va 6 vi .f,\" ,-,

t&i quay. ..,

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hfP ki h1fu lU911« ... ,"V()1. phep 'tie

dall 40 -c,agi8 trinh bBy dQi 80 cac vi phUO'J1gPh~p pn6n 1091 ~e .." ,." cae so nhC)1,P,1h ~

rieng

tr:1,

gia

,

,

. A

. la cae yeu to cue lchuJ18

dien bl~u A."',,- 1 tll. cue JIhOm cIQ.J t .11& bit Cbs ,cua cae -.as II1r rQincare, , dQl cue ,~.

.

' 1'" en ~U th\1c

o1eu

2.- Cae Sp!nCf Loren t Cee spina t 1 $ian Tee a phllC he h1tn ,..

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't~g cue SI,{ 2. C) ,

- bi~u d1'In 1Ih.ang.'t IIO'Agduong

nhq~ SL 2, C) , " CO hal ( '.A ...'", khong gietn bieu d1e1l khac May do 40 cO .hat

spinal

8pinO' oh1ral-'t~1

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khaaS- ~-d;i;)'~ Cae eptAO' ha1. thUh

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DW1 pbip nstJJch If~ toe. 4~. spinam cbi

tren

ct1\1,ln thanb ~tDa

1,t."£I~Tiftpbep btln ~~1 00 cb

l!-6 c!uO1.

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ob«. n~ phep blln.

co 4

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0: IIIlOm

t11p cua nbO.>f1'otncaft v~

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t-i ch~n) dua them cae 1f1 t~ $piDC1(Ct.

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lChoa tmmg tJD8 'tCi'1

pha. biG 0 '9'4 cI!IIJO&91 14 cae (thu9c

dB! xUrig;

cae Mom Lie phan biG (graded). ~" CUB Dboll P01noare Vi pban ~o , g8m oa giao bon ct;1 aO nay dll9'C ~1 1.8 nbO:mdeu

8

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c1

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4.- ~ieu khBn~~~

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bay ct.i 8 ""~' dOi Dmg. phan 1001 oac leudieDuat ,.~ bi & slc¥ 401 xung. eu vaG "1a ca'; boson va cac :fermion n~m trong cims m9t sUu da. tUJ.I~;J va cO cims 11116:1luvng.

dot doi %Ung III1nl11a1 vat m& rSiDg cb.m cac

s~ i~ t.rsmpg: ..Lrongt;Leu III\lC nay s1Cu ~81eukhiiDg gian Y8 (N.1)- t{, splnO' 1 vi khong t08 d9 been. c&e toe d Q spinO' ph8n €1ao gian. ][bong

. cae

eta

teie gie. trlnh 1187hbh tbalC 1. vc11 slall tmang StEIl kbang sian ls kbqg1an thO1. g1an thOng thuDon.s . va ls BUu traang Hlnb th&ic 1ujn. slau tuyen

cac 'tzuOng ne dpm trang SUIl

traOng cho phep mOt~ 89n gbe tbQet

n

cac guy tIc Fe7D-

cO th~ phat b1~u trio

dol' %Iing. 1.egrangian slell bien, b(t 1i nh1'u

.~

cu8 kh6ng thO1 glaD

5.- Jgom con1'orMl:

1Jbomconforlla1

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,~

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lofD b(t .Ugp tbeo bLh ng& ngii 8:!.e~ truoemg. ~ .

.. 18 Dhomcac ~ep ~~ d01 't98 d9 bao g~m: - cac phep bi&n-a&l cue Mom Foincare, - Phep Mill ,

dA! co din toa dQ ][bong thCn. g1an

..

. ~> 0

(I.2)

lIhom conformal

co 15 them 86. cac v1 tu. 141'i1,&\'"~\

I

,

D ..

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va K}\.

Sau do tae gi~ trlnh

18y d,1

86 cao vi

tal, gisi

et~l (I.2) ya (I.3>,.tr1nh

b8y I-

tT(-x} . 1-=.-c2x2 (I. 1) %~ . ~ % ~ - Phep bl.Sn etAl eon1'orma1 dIe trung ~ . or.1{xl (~ - ~ x2),

Jt bieu

II cae

A

II

II'

L bi.u

a do!

.,. cna toen

cas Maclcey, hr

.. tmcmg

Salam de III doi YC1 cae

dien cam 8inh

,

thIGhvat Ii oao pbep'b1fn , phuO'Ag phap ao dtnb phep billU.l 401 cua ahom confer_l.

quy !It_" lut~ .,

1a ..

8p1AO'.

T1 ~

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6. - ~O. auperooafo~, 1IItOa~omu. 0- .ahOa00a1'01"881

..

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tl..m bop YJ _0 .tJtb cf41 84 8UpU'OOllfOr8alII.

.. DI too thimll do1 .& kla ~ S ooafo1'1l812 n tw ap1DG'. ~. cae hi trinh -7.

Cb

U.

(2f

sIiu WI XIfBGJ! ROBO .' ~.~

C"'Q nhna

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d:r .. YCh~I ~ &91 Dbo. 40 18 81eu 481- 11. 1 (I

cao Dho. 81eu

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cO thi

tu. &pUla (Ii> 1).

]flu 117 »ft

Jl vi

all;. d11a fXI8b c~ clSI xUng t1"ODgSU(]I) ta 00 cfel s4 *'

aptDCt be Dltft cua nhOm 461 ki clSl tg sp1Da @ 18 81811 *'

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thl8mB dol ~

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bay acbuung I II'" ... at an ~. 1 "Zm'Ia' ~ la 110'*g

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Sf (]f). .

.

-~ ... 1.- t nnh mag Po1ncar.. h1.jQ 86 ...1 1a; spina). ~g bilu . ., dot XIIIIg110'rOag ...t hVJ»IIOt each kb&tg tIa khong thCtt g!.8D va 4ft =a hong . I 'fruimg h9P 40'!1 paD JIb t oua 818u QU~D1Dg...,

rOD& :a8g ceo hi u.Rc pb8n giao hoD

18 trWl1g h9P steu cI41 Dug wb rpng kIt hgp Wi

sue 2) CdS1 ~

.,.

.' 1

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.. t%'Gag t rwag

I bch

Qfi3 }

hqp co Qua cae ...1 tal ap1Da Q()(1 . 1~ 1. 2) trung tam 00 dong:

. - 21 ~i~ ~ecp Ii - 2ieU e..

~;S

Z, 1l', (II.1) (11.2)

t Qo<.18 {T; . ) l Qed' ~

Q':j ~ /3 ) j . ~ /'=' )

j . 2~1 (vf~-.

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en.)

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fI!

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die trung

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bi11 khu1luogng m Va , 80 l\l9Xlg ' - xmlg .

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If! dui

kbI qQ7 cu8 do-1 at) aie\:! (!ci ~

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~t b1lu G1b bit " merr~g SU(2) ~~ " .. tllBuperspin Y va Buperieospin~. 50"(2) 'A eas

(Y,T + 1/2~(Y,'-'/2)E9(Y

+ 1/~)

~

(Y-1/2,T).

I) tbazang J. JDQt bien duvc g91 18 c8c hypermult1plet. to dieD bat kha quy Db., Bau CII\.ttrUc(3, : spin, I,1soapin)

{x}'\, ~i

t-e-l}

(1-= 1,2)

(II.4)

2.- Steu Ichong gian lID SiBil khon.r u-iAD- Stell r§ng t~ ling tr.Km~r ven sieu dS1 X!ing SU{2) co cae 1;98 ~~I

.

r

%80 dtnhnhU"

-.UI.

.

.'

1 . exp(1~ ~* e:q>{-1 (ZZ+ zZ-+'J exp[Hit"S + S~}]J(

(II.5)

1

.eJCp[i(~Q1-GvJ~(o)cxr[-i(qG+G.¥J]" expr..i(~S ...S-iJj exp[i( zZ + zZ+)Je-xp(-i.)(J'4~J da 4n Teo cae.Q h1iu Bau d~ phan biit

2 vI

trong do ta tlr spinO'.

8.!!

!! Q

S co(

co(~

81&\1 ~-raCtng H = 2 (Tilt t&t 18 2-sUu t~) dlZQ'c

- - 2. -

-2 Q..< , -

.lJ...- ~f .vo( voc.::'

, CK. .A.- , v~::.

~

2tX E -f1,;.,,-.

-1 Q... QJc " 0<.- - -6-';'i, ~ = -&""

va de r; h1fu

u..;.7)

~=("$.,f)-'~"ZI'f/"Z)

Q", 2" Q.x ~ (II.6)

, .

J.- Qpy1ait

T

t:'

.fa

, . U oftUAe4e TM MC n"

toRn

., }Jam trm7p~ sUD.

dot'

hep

(II.S) .. ruoarw T~ aA1 eU4

p. big~

(leo)=- tp(O /0 ,0,0,0,0)

:

"'

'"~"""-

, ""7I'1D'ilia rt)J1' '~~-~.'--'--'-'-'- ""

.

SU (2) i .

'f/Ii."> I"""""

1"'f

f'~"\,.~.,i

.Ili.

I

nAIIJ""f' .. 0 t;r',I"..f,-'!..J.Ij!.:'nU~ij "c' !"'r\"""\ ""1 ,'. "", \' 11i\.,:It.:~:h')'.\..t" N ":.~ ~...,~-,

! :"'.. ;

biSn dAi d~ ,,' 1;~ dot ..'

L ", " J

t. 00 till

rUt ra q\:.y

irWq

80 4Pah Db" (II.5)

d51 Tas. cao phep

tras

bi'n d~l -81 day OU~,tell :

(II.9)

'

.it

(11.10 )

/o("I"T'

,,~.

.

oc.

of

/

(11.11)

'" ;, %- ~

J

= i~~

-(?o-Jt)Oc~cp-2i~~~

Tat ~_Uu luft 'b1h d&1 ~ ' 30' ,Q~ ,Z [~ ' p J = -, ~ 1> [SOl.' s6J = -i ~ + (CT~~)~~~ , ( S~ 1 ~] = i~ - (t) oa/4'. () [Q-.,1J = -i~ +(~1t7} (Q~lt]

l

~~

(11.12) ()ML'h-Zi~ ~ . T

.

(11.13)

(II.14)

. [Z ,t1 = i* ' [ Z+, ~] = i * .

(I1.15)

,

11"

.

cara sinh cus »a~k.y.

eus cae stell

dIJVc dtSl

.,

D~ dm quy 1ujt b13n d~1 cua sUu . ' traOong

.. Tc71 080 phep blCn dol

...~ ...1; qua thu truemg 'toan tw '- . tll ~vaJ:-:

[Mh\) If]

,., ling v61. cae vi = _f 2:h,,1-i(~~v-x~C},\-f(e-o;,lI)~2...

1'"

~'?< -

r -- -.1 . (

I (

II! pbep bi'n d01 oon 101 ous d~l SQ, II cae biel1 dbn ql1Y111ft bifn d~i d~y du ,., tacmg

t' ~ . ~

)~;, --- ~&-

1 " - - z.

I (- _ . /, -- cr n )1" -x 3rz"ft

-"V -

.

) 'J

(

J

~

(JUG)

- i(t}~" CJq~- ~~f~" i5)t'r - i (Q5t~rr>-rr - ~~~II'l)~ + ) 0 + i (~~v{}.;z. + I t1-~\I~ az,

rh r

2. ~,,-&- ?~" "'if!> 2. ~t) (

12

+ (Ih4..6.)

VT",;J=-{ T(+fC.!n'i-'l!.\T (~-L +;;- a_

..)]

,

.

~

u~

L

'i)

J..

1

I (

r

'

+ i[(it-~"if) +($f)}(),M "'1: (* -7rz)~ - -- -- -2: * - '12 '? i.

J

.

(11.17)

[T2, 1>1==-{TZ + ~I(-&f.z- '?~)+ (iJ~ -~: 7~- - (~'1 - 7~~)~ + ~ (~~+7?):z +

1> '

+~(*+rr?):z-J

(II.18)

.

fIV ~tr :-'£~.:

f T 3

- ~

( T 3 t1\J -

\ ( 3

.

- - t

+ 2- ~z;&.+ -&a~ -~ ~ - ?ail J +

d , T

+1 (-e-~

~ - v~if)~,M - (&'l).£... of-(-&if)0-

.

~:Z

- 0 '\ .

(II.19) At 3% r J

!>.

1

0('

m!n!pt

.

TIl' kha1 ~r1h: 2-aUIl trutmg

2. ~(Xf-f-,~,'1.,'1.JZ) =2: '".",P. "1-= ~

(11.20)

-

"'p At-I

{tn,n)!..

tJ

p

'

0( J[ R

tzA 'f(P'CJ)[«"-I~faLB'l-,Al(x z) ,

1l.1 lit'! rtl-' /"'Y\

d~1 d!y du cuB aHu irue-ngt

bien d~1 d!y du CUBtr.img

thMhphhi

ta thu dC'1

vi dy.t d61 vOl 08c phep

V80 cae quy luii bi~ dU'Q'c quyluit vc7i cae phep bign d~1 do! mg. b1i~ d~1 isotopict

ie co:

7C~0l-;-i.?".

~

[ T1. ,

] = -1. i 1..!L Cp(P"I)[o(~pJL~J\!(X. ~ 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) (-J.,

'f.(P'~)[~J( ;j..,l ( (m,,)[a(~l[~..BJx,Z, .

+ Z.

2. p+1 1(m,")[0(0(...1(}JIIl n+1 tM-t,It+')~l[oc~J'z

(x.:.) +..f

."*'

I ~

)(

+ T . ~ '(\!t,.,)(~)U)J.l

'-.

(_j)f P Co("",Cf...i)(~l[citj11 ~j)m-I+n+

x ~(P,"-

.

.

' ~(~l(A.l rl!J-l, h)(ec...JC,PnJ

(J',z) +(-~""(n~:(a:.~aI'41-(p-4itJC~l P

".,.

.

(rr.21)

.

1 -- _5 -; tz

(1(,%}1 '(",,".i)r~1~..1 J I . ...!!-fD(f",lr*,JfjArll' Z ,"",of'(~I/..iJ( pJ(,.J'

[-2. ..1rA'[~(J.;.,J r , Tj,.,,ft)[C!CcIC,..)[fjJ..J(r:,z)) -

.,.i (-I)'"-!L-

2.. .

- (-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)

(p."

~ (T,,~(P"I)[cit~(.M,J (J<,z)l = -Li(-1f'~(a:)~~a}!

.

/41

t, """1f-",)e,,,J

'o[~JfjAJ ~z) .frf:1.'I)-")[~...J[}.A1_-

.

~

t

.

T i (-1)"Tp("q1( ~),8}~}lC'f(r",-t}[...,)[jJ (x, Z) J

.

(""""")[~J,.1

crr.23)

tren,

b1en d~i va d'S1 mng trcmg cO lien.

ta thSy zoOr8.ng hi

Nhll1 veo cn CIU1hit cae d01 XIiDgthong thCrl. gin. vOi. Dhaa JlQ1:each Chtt chi. -,

~

-' , 4.- C'.A""t'

..' hAt ""Pili. "'U$

' ).... CD(pi-t,lf-of")CitpftJfj.,J- ft~" rM-I, )[ar...J«<,&\l. 2. p+f T Cftt,n)««<"'Jf1P"J [x,z)

1 ~) 10:>

<0 t P( )(/~"Z) ~ C1,'t'

...,

">

,. cae b1(a

..,.~ Is cae toa .~ sp1Da BajOftDa Ya Dt 'trung ti1lab')sng o. ~ gl.a ibilt bat t1u;c sa" 461 vb1 ball ba1 411.

hOD~ ana (fa tuyh :If. ~:xet ham ~r'~v !tal entea ch; 'f:hrpt!Vl1'!lal',AI!h",m i;11'rmlr~. th~J'th ph'» a1~u tru.o..g.

.' .'1., (10 €-;7.. tror~ bi~u di~!1 vcn deh cuB vacnuua. 'tmGDal sUu

ou1 108 cO hi

14

.

,

(~,~,'l)P(y,t"5)lo)

=

(ot +f(~-i~,."e-

-i:~JI"'l) ,(+-'t),Ct- ~y~(y,o.o)J~" (;

":-)

(11.24)

db ifa

,hll'aDg U:bIa ..R 461

"

,

PhuoJag trlu .., t1'W'Ag thUhplah:

i«t

~".

(.)

Ted cac

«,.l[ft

...

-nfJ. ~ (pr"',~). ~... c.

.

,'.'

j

/. \ ~ ~ k- ,-O ~ ,;

1 1ft!Pi!P!a! -.

I {; "'~

"-r

-tl

-~ -'.( rr~ ~(F,.~)

(X")/O/ =

~""... ~ 'l

'(~'.""fJr~"h,~J .

~1}.~

a'" + V~~JI"

(01 t i -f(~~fr~~ 'l~'lV')+ ~tt

.::,.

) 3 + ~ ;;Wi.,tt;r" + ?y~'{JfiJ J . (ifA.-?;A.),

--1-( ;-'1- ~'~) ... (~-ff{,."')(2Jtz~!')"., tft!,,! -

. ~ L- """:0

. eII. ~.5)

.

3") x

()f.'} \0,

.

.'"

..

A ~-

A

..

.. 1-

h..

hvO'Ccua

oIlY t UBkhu

(

.aaag cach can UIUlg b, 80 ~\>- "'",,',...~

'P (0,0' . > fc(",,/J) '(GC,...ee...l(j\""nl(X)

nhau cas cac t98 G9 spinata tbR dl19"=cae h~,th1iC' g;1i1s eic ... v- d~.. ham t~ khao sat oae luy thDa bio 2 ta f

i: ~:

quan ha1 c!1~11cua cae ~ thanh

(n.26)

-f ("4)~: --0.1

-i i (1"IYst

15

p~.o - tb.:c 'eau th~ dlfllc cac hi -+ !(ys)!

( "\1.0. A(I),

l.t{~);S(X?I= -\,4\~(~t(,,91

' <"IJI) A ~ ::- . "r8lp(;c) ()(1);,

/ (I) ')

.

-i (/ffMts-t

(II.28)

ill(

(II.29)

(II.2'O

< A (~) < A(x) ,:(":")> = < r:()()A(x'» ,

(II.)O)

= <.&(x)A(x'» ,

'f~'~ (x') > = - < 'f';'(X) A()C')> ,

,

(n .)2)

< A(~) F(2.lx'v ::; < f(:Lrx) A(~»

)

(II .)1)

(/1",»

= < Gal,,) A(x,>/ 1

< ~(~)

(II.')

(A(x) A~)(x/i'; = < 1:1.,::) A ()v)

I

(II.)4)

(II.)5)

,

eofc,o) :: A (K) - J (J'.)

co(1,0)- :: 10(. ("1.)

"f 0( (]C.) I

fi,,1 +4. (\c1p 6(~1 + i(~c~p

";..1» ,

16

1:rcmgdo 'ta 'dB.Jri hifu:

(0,.)

J

,

'f(:"" = 1.!- (f', - ~~CX)

.~p ()()

~ (:.,

( f"-.,' -'\ Jy"-J

~(:') -'~0c).

. ~ (](,) -r, ~CApJ:i( ~) 4-1: 'j

!:IC~

Cl'r

e<

I

t (,,) (I) :: A0'(%) (0(0/2.) - J..c f (2-) . .L( - T ( X)

:: 2. out y

Ct:!lmrta' TIT. A

.. 3nu

XHONG GUN HARaDXIC

.1.

}O nhuvc

thanh

ch.1la que nhUu

phJl::! :Ch;a1 trieD (theo ..

, ,

thu c!ll9'C trons tieu ~c Cae h~ th.:c ma ta h9C 1"0.rang: hinh Cluing Is bf qua c~ I1~Y cO ., tIs!! 'QuiD. bitt ngbla tieD troDg !lieu. khong glan.ar, -r~D.g.

-i.

.

-

cua

oae

~tla

S1eu. tnrCong me dt.nh trcZ1g Bien 1chong gf.:.aJJ (II.4) Jl."'. diem la '."

.b.. }SC lay tQ8 c!Q spinO' vO(~ I -e-~ Va co MIln thanh phb spin cao th i:ta. i)~ IDat~ cao hypermultlplrt superspin c~c d1'11 hil11 chEl len nhien, vl~e eM nha h~

thgp.

va superiaospin ph!! ~~t c~ tlVong

thuy~t

th.zc lu~n stell trl1Ong. . kho khan trnng :,at bien, n~ien vl(C" my cUu 1; cue hlnh d!;Clg cae Lagrangiu tlZO'ngtac nhi~u big!l v.v.... hi~p io~

Jo do dol v~ 81eu dol x.mg mD r~!'lg SU(Z) cIA co

,A

A

A

,

'

.

.

.

t

v~ Sloell

rt:O'Dg

gie.i

sac lu~ s1eu th.zc tnrcllg kbac. cl:c. co Ll1ai kh6ng kell! thee ph~n

1"7

hkh ~:.~u kl~n h~n chat ~~ ttlang ya cae in. Ogtevetxk1 thuc trWng luij.n steu " Tao ~a1 D1~m 81eu khong glan ha!"mcmlc doh.

..

'" ,

'I; w ~II

"'I

..

u.~'I!a"":

1.-

,..' "'foIchl. e1! ~

':""~,II'jC\!,"" va 1: "ft

,~:.-ru vat

dl:U4 cua .9 ceo phep b1h neat

.-: h'JII (II..)

18 khao Bat

kb6Dg paD con 1tb1 46i

(IIi.')

, "1.~ ' ~:, -+i;e.2. 1 -&1...; i~ 1

.

cacsieu

nonS slea. Bhang g1an con nb

i~ 'Phh ~.

hone ~rahUn.

00 hlnh tbac 1uIa

dUng ca 8~ DB)' kheng cO dnh hi~p bitn

vi,f'c.t.lnt';l£ifl:l,siu de:1 rie:.t' ;:~.Lnng JT. '2 kb6ng pem .

'1d1a1f:r1~n,~h 81h ::..~g case.

(XU.1)

chi

thiza !1l'>indlS1 xUng trong 0(2)

(hey U(1) }.

vTt81e.u. kbang glen harmonic ls: t~

. dUng mOt 8ieu so d~ng then. dim V80 bien

(:rn.2).

tf

.'." 1'~~g &Sng g1aJ1' COIl

.,

'"

a

..

StJ(2} .

bsJ' 1i thuy't

lien hi cac bi~\1 di~n..

U(1)

mc1i d~trlnh d~c'btft sri(2). Caa bilin so a:1i.phsi vM c8eb1~1i. dien o~ sr;(2); 40 ls cae tQa d~ harsonic

80: ~ <1: ~!ij6

dLrcY1dQIlgbi~p bi4n

1

Sf! "'---

St;{2), j: : chI s8 U{1)). ..

,

~g,~t.chl '.,. . t~~ d§ bar.onio .cue u.i,8~ ~-~msn~ tu. b1~1t !'",Ii.- SU(2)

cae YO'huang Loren Va 18 cae y~u 'to' ch~n it...'" J( . .. ,/,U.JO'cacbien so harulOn:!.c, 00 the cbuyen thaxm bdu

laeac ..

'\f+:i;1f~!"'f,

."

di~n U(1):

#

,

'f'- = 'Yi u; . -t f~.

..

t'c

'V'lphb.

,

{

VB Bien t:rvenw mAt t ~H CO'sa

3a~ do ~3cg1a t {oh ..

pi18n t'heo u. tLeh"-

2.- ~ BO'J!'i~1

.

.., gi81t:lCh.l8 cO'.a bao g'Omcae t9a d9:

,.

-of- -+"

-

:t

en!.2)

j l'x.a 1 -&~ 1 -&~ '

-- } -&~ ,1t~ -' Uj "

-- - -

<

18

Va DgII9'C 1011" . "f' = 1.4+1'\f- - u-"f' ~ .. . . , trJ.nh Day cae tJ.nn ehft + cue 111 ,quy

'

i

. M

, ~I

~ -

)

0(.'

. Stillkbang glen

.+

/4

+l

con Ten cac tQ& d~:

r /It. , ( "" = )(r - 2.r ...uri»J . lAc,L$j) , , ...Q..1;:=' -e-fut. -v~ -+ - f . ~ ~- = '6:. u. -,-V-. - ' it:,

S )(A ' ~CII. l nO 1& k!n dol Wi

. do1 s1e\l d51 Ding Sa",

got 1& slell ihOnggiaD can gist t{ch.

(III.J) U- J cac pb.p M;n ribg va ct.

'

+ -+'"

(x...,-& 1"

, U-)

::

~ (i) .:t.(ZA'U)'

(III.4)

31h ~1UOna :zac dtnh trone; 18 siill ~mOoag g:tal 81 en kh3ng g:t8lt cen gi81 tich:

SUa. 1;mdng g:t:l

t:Cch (III.4)

khan~ P:-;9 thu;c -a-, t';.

.

g181

t[ch

va 1101chan.s ~ DUIg "t!ci1 1](1) Is. q. S1en tro~ phh cO 1d1e! ~ rJ.ln

-t{ch d!lllC sgl ~ J; tlf' ~ = ':t

nha sau I th4nh

FCII' ~ '\U(q--t) -'1-~-('i-" ~('f) ]! (~/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

:;;Ho-

.. \~,IAJ

'\ + ( i+.e:+'-a."!';;"(1-3) /

~

- ("AI")

+

(iJ+-e--f")

( i't-~+) 3> (4t"'4t'St./ 14) .

(-e-"t.+)-ft+"'.1.(4-1)"

cae truong

(III.5) , .. ... pi}\1 ...a- tts8Dh puan trong .. khat trien(III.5)

cac t9s d~ harmnic,

tr1~n th~o -

00

(III.6)

.

1.1.

.f

t9a thl1~. 118)41 cac ~a xA' C~)J1vea cac

~ ) .

d~ h8Z"1lOG1cuf . ..at L (i...

%",1&"'::0

);; (~)

. :1- - ' ~J ("f"'f.1

'1".

.

cac t~

feil'"

1n'tq ;11

() 'P q (

1!

-to %" va 18 Me 11111.1d1;. 4~ khOu& thOotg!sn tballli phln de} 101 co khat v!. dv. dot vO1 P{q)c.XA' uZ): .., - 'ft"'" \ ...J..) + ...Ll J' U. n ;}n)(xA) cbl conphv. .do1 kit. QI.1Yl1oan toM bit

1.soeptn.

wi isosp1n.n + q/2. Bhl! Tir, m§i; 8~~U tmODg ~ Dhlen t;mag chi t.; Dhlit, cac 18ospm cOn 41 ~ o8c

'/,

.

,

tbfc

tv do b6 ~rv ho"c C8Cbjc

t\1' do sause. ,

:mng cuaSU(2) gia:t t!cb.ch~ Tah~ ~iil 1$1 c~ 18OS'pU1~~ ~ ~c

.3.- Mq~ ca~ t/.'We~.muJt1-nlet

c~ ~"'g si€cu t=~~ t!ch: !d~1il d&i. ~r"2 7~U8 chUB 1aoftoublet gi~i TQ huOng 'fi H7Pft1IIIlltip1et 1.eosingletsp1,na D1rao

.S~) 188ii!u

tren TO kbOiluvng. S1.eu 'tzvGong gLS1 'ttcb 'turJJl& tmo.ng

( if' <'>.!

.Hyperuw:tiplat

' ui)

18. + 'I tfcb giai : ~.

q+ (ZA vobucmgj', iaos1:nglet iaotrtplet 'leyl -t hen iaoa:1nglet spiDO' gi;1 tlc'h :tacmg aing J1 sieu.

pbac cO tfen Den Ho--S1;ell-~8D4 cba va

vo buC7ng ;(1.3) trag lith thvoc cO t:lab vo kh51. larzng. nvOng giSt t{ch

Ie

.~

(.I.J(ZA,t#).- S1.en t~ v *CZA-U %) g1al ." , b~ng 0: ,

C, 1aodou'b1et t{oh trm:m;g c:huan chiIa :l.8os1.Dg1et ap1na .jo~

. T1rC'ng Ung v-71 Ii

X va 1aos1Aglet thOng th.a7ng.

thu7ft

cfldn

V++(z.A.~ u:t) dU'~ ch9D- 14 thl;c.

~

;(1) tU'O'llg mg vCri hypermult:1plet vo huang ph~c '-~ctC' Tjt'\

.'"

,

'

h ..

-t

i "i.

4.-

,",eh~ than P"!I~Acec,

.

,

tracm{l

si~n

), R ' C SC

:

~ CoB --- s1 A t mcmg ell

t . rllO'1'l~ iron;:!

..

~.. rant; btt~

C'

II

aJII I~~, ~n - !ch vi . i '. ". II cn'l1 k1~n I1p bO1. cae .'."

,

..

~

'-

..

..

,

ch')'do t {cbkhorg gi~1' '.' '"" do do1 VO'l. cb !.mg. ~ , . ta co the II dol vo1. Bien tra

",,'

chU'O'tlg giue 'liren TO kbOi 11lQ'!1g., JIbe, phllO'Ilg 'trbm vGi cae bype-rmult1plet ... .. '. b1 ~ CllUYEndvng, ts co the en dien caetruangbO t2V qua -vt se ttJong Ian eae txuang 'Vit 1;.

.

..

A'..

, DUag phaoong phap J1h:r 'Y§-Y, tac

jl. ... ~

qaa.Dhat dll.

g(1ia cae ham t~

th~c.au

, cae eua cac tm~ vI d¥.'doiTO1 hypermultlplet

hi tron~ oaeb7P8r~ltiplet. 1'8,.81; - ,SO!m1U8: 20

gta da thu duvc

,

(Ill.'

,

(III.c

< Cf~x)'Y(x'» =-< 'fcJ(}f~j(') <

~

<1f'(,c,~ fcX/)> = < ~(x,) ~ ~(~)

(III.9

= -<.~(X)

'f;(~I»

~

(~\~~<'f(~) 1f1x'»

{III.1(

k

,

<

.

. k 'f(J() Ap,('!.lj) :: <~(J"

i' '1'e](')

.'.

(III."

tren vo Ichc1

:;: 2.i~Cf~x)

. luvng)..

k ( ~(.,.) Va..do1 v6t hyperlllUlt1ple-t Howe-Stell-To1msend:

(III.

L;

,

fC)('» th(i';) ,

,. (CfC)()'tI",)} = -<'f~"() k, It "'(X); . T (x)t;(~!}/=-

~(',e)/-'

< ~.P

<

'r(x'}")

,

(III.1J:

,

(X'» = -< 'fi(x) < -

~ (~} 'fk.(X")/:-

< .(X)~i < Cij} -

(III.1S)

.

(III.16)

.

< $(

0

(a;. )Ot~

-,$ 'f'(IC)~ (Jr') > ~

"7.\...

"" ceo

thUc

tbl1 dtJl1C co Y !Jghu

rnnn

h9C dan

gian:

trong

SiEhl

Ichang g1.an .

hi qu8 cua

DO 1.4 hi

bS:t bioen tInh Uen

COla 81a1

t{dl.

(UI.14) ,.b(ij) 'f'k(J() ~ (".')

21

~

~

"'.ft

"

hiSft

l"""~

Ch~ IV. ... ." HIP JiIKN ~PO.B.ii4L TA StlP:u.CQ.NFt'>~ cui CAC aO B!JII !mtOllG

.

coni'orme.:

dp:h

1

aua1 1.8 811 rJJ 1"9ng cuA 1chai D1fm h1~p gib

cua Ii

cae 11 tbuyit ~

'tieu

.- Khai ~i~m VA 1;~en eblNai hi~n miJr. hi:p bien conformal aye ~ tac bien d01. tllang hong ngbta .. U~u muLL hifp bien confo:ral 'truOng, c4* -n liVft cbuLa 'ria.

&

..

SIt.

4;;huan Mfn bip~~to-rft~h

:1hzc l~i tbu,ft tM. m&nole Ueu

.~'" _t -.eo

.:qmg cao

ban: ~o~ ~

li cvng

cae 1 III- sl1perco..uorma. -..bin ~nb d' 8811: BI~t

t~~ gt8 Mil vA cb.~

18 doi xt1h~ 811perconfor~l.

thuyet

1;

d~

.

. ..

2.- ~,p - """ "" tl1uyet co do1 t1~u ~c Uy.. La!Xang1an 1; 31eu d81 .:x~ ~ dbns then bi~p bi6n confor"" th! mal, Tite nEu,

ta cO the tlm vI d,

c*c mOblnh co dSl

~(, ~~ .' '%ling

..

'c&cb cham! ~

11 tbu1gt

~.

do1

8ie~ bien conformal, bo,e co the- %&1 d~g ~'c Ii

superconfor_l~ng ~ co ~t 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

ib.1

t1:uyet. DO J1. ph~

p)Jip d~c

stell 461 %ting Te %81 d~g

.

..

. .

3.-- !~t

s.q 'Y! ~~~ng

~c nli,

8u1 1"Ofigs1.4!11d61 tron~ ~bnb8V hEmb (pa-""tner) :mng cu~ 1; ~. 0' d~g e&c ~6 hlDh super~or..1 cad Abl9Vt .. Va cua taegia (um ~UO'.n,£ V).

.\0 t'c gi. d~ 't!nh chit do1 ~g ~!"g

uiu tri» ~ kh4o sst 'Yo h~g

~lral 81ei;,dS1' d~tn d§~ lvc sHud6-L-

tv tlrcm~ tac ss3...a 80 h~ 'CD ~8-ZU.iftn.

afDb Q ch~g - "upereo:rl"ort:al ~.i D.ag

lCin)la cuB JIO hl~

22

Ch~. y.

.

,. . C~C at:) aDZE LY mu"d'!

r:u.;v.a ;XJOOl _rle;

conoRJUL VASti"PEiiCOJFORJULAI PHi 1fJ -rr: PHd

6.""'" .

.

.a .teu <161~g

DO! Ding oontorllel

ct_.. J... ~c

dol cao. vi Y~:r, t1b1h01 phi! na,.. C<1chi P~1I3yo. dlJ"'!e ch~ e<7

I

-

. -

%ling thi h1fl1; nitng 11JQngr't CQ coo che pha ~~ c&c d01 ~ y den nh1lu Mat h:!.~nnay d01 Yat e;e 151 mn6~Y Is ,. '.'..' 0,1 che phs va t~ phat ~a 1Astanton

J 1;,1 cae ngbl~m c~ 1ien tr\rong.

..,

-

1 , tun " Qua phllC1ng trinh

.-

"

,;;.,.

,

,

,

'IF 'a1 tro cas vacuum k:hon~ bat b1.en t1'Qng cae 11 ~'_.. ,~- ..~-.J~'

"'.. " ' -c'. S "p" rc ""n "'or -"' -« '~

'".<--:'~ ---"'-,-~",- -""'"

-' ~,

,,;;- ~~,

~ -

.,

TJ:.t "

-. Inn .,....-

~~:::>:d'Jr'YJl

1

"

,"

'Y9ng VflCCIUI t!"

' 1t."

kh

khang-thO1. ", can tll

G1& s~ gia g1.!m DehUIl. ttifcY b" - .. ang ~vt hall! e-gQ Cas ong v~

1y thllyet t:I"\ldng YO bU'l7ng -r co i.a~7:;".l::?i::!cl':'-

trong " t Qua lip khans

'/,.,1

jO""

:::

t98 tr,gt:1.ngichac, thO{-"gianl

0('1.) ,,/

I

i!), ~iI;) 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!

'

.i.

",I'

..', t'l nhUJ;\. nguC1. ta ngh d~~n'icd~g

~t , each r~t l~

nhom con bIt bien Cll~ va call1l.

'ruyJ;h!en.

,

{I.].)

bien I!S1 v.~ nhom con ~'o 11&~~ hbQ~ ~0111"9r_i# Jrt~t r'" ~911 Po~~ dU", ~1 ~ . 1!>d>c

1

,(1'.2)

dsta ,-,

'1IIJ1i!chac.

trong t:ruang con1"ormal !chong t!m tI!00ng qI18D:taD, ngbi,im h~ng so cua phU(tngtrlnhLagranga-

t~c ~c. const. Jd18ng daa th~1I net gl md1 vso 11 thulft. bAa Db., cac 11 th'113t ~cs 8Gler ~6 411. kh8ng 1:&. 1:01.

23

cae t]."Wlg bin)! ~aCQU1I10',1 It\ng a~ MP' Yil

..

.

~

.,

,

"

bH~noua,

. cbQn Mom Po1ncar~

ma Ch.9n

vacuum 1:a khong ..

..

" sinh bC11 V'1 1011'Jt,.AA)) va

'1 1;~g hay cue Fub1tt1 lei dUng lam Mom QOn b(t , Dhom

'

1

1,

eV.)

)

Rf' . 2(a

Pp + -;- X!" dei). uguyen d§

deS1tter

(a Ie b1lng s6 cO tbu

Dnu k1fn bat 'bien RJI" c~ vacuum din dgn ph~g 1orinh.

(olrcf>~)I~JJ~/=~ ~ ~~~%,f?dxf'tJ)~)} fL

=0

"..

,

(V.4)

" Wgh1~md~ng 1;hO1.cue pbacmg trJ.Dh (V.2) va kh3ng tBm t.ht#lngl dput ~ th~6.cS

.tV.4) (1)ch..mg '1418n8 86

(

,

1>6.. cp c IV °C1/g) v~ trong thai trdn

bt3. O~o nghi~m 1nstanton

Eilcl:la'e b1~n d~

cuB cac phllO'ng triM t~g ngu&! quan taIL yi

giG:l hp bIng (u)b

tan t~1 v~ co, nhfmg d~c d1~X!lrat tl1'C'I!g .tng T<71nhimg ofu blnh t~ gian va ~a then. g1an U.nstenton) 'Pc + ;;' tU'O'Ilg tac co phAn dong gOp lUn cue cpC, cc>ntrnOong da dtch CP" b1~u ditn nhTmgth~ng g1angluvngt.1o {bey giahpt) nhnu rat dll?c c8u trl1o ?BCUumc~ If

chUng lien

tQ.P,,'"

.

2.-£Q bin!; codQ'1 ~g

su})eroonformal

b1 p1!a -.:&1011

d~.

slen ',46,1 xU-;I'lltcue J:Yj"t;tn:ygt

t~ .blt ,i

nhtr cac 1nptan~cn:Aku.lov va pa£ihnhev 4'ii ~y kheo -at m5 blnb 8uperconfo%'1D91trcng Bien khClng tian (1,2). lito r3lnh.c%o1.8 .-~sl1yr~ bit ~1. ~ 1 _no 'Conf'orma.l«::<1h~e l~ .. . .. cua .&J1aro- hM.;'t':' bien oo~or_l)

.' ... Pul."

,'.

24

:nt.cmum,cu~, 11, tpuyet da.n cho th8Y ~u true,: ,Y~, quaD de1',tv!Ji d' tbuy~t, chu~ Yapg;-~g;J,.Sf'J;I1~n nay co - rilinu ~ll- chi :La 1'«1; ph:rc

t~

~

»1 co c!.!!It~o

110,hinh IIIU1g~,c bvng caS 11 thuyet 1 chilathong g1an n~. hong

!tDh4t

ulu ~ trlnh C&,.vl~c BY dqz:g m6 .

",

1.

1dtOngg1a~ (2.2)

co

l!o1

tl1 phat nno. cac 1l1Btanton.

th~ '~1el1

~t; bien. cozU"orma1 Ichon~ thO1. g1an

0 tron'J

tac~ Dif}~ni7 tlc g1s bin }j~~n 11 t}1Llyit ,tru&ng tro1!g slea 8V.pt).rcon!ormal bt- phfi * ,~~$ Xu.$t t>b'~ d~~111cua 1o'c 81& l~ Iagrsn~8D o~~t TO h~ tr~ ~Q1tdQ bal, cblaul

eV.5)

'0

chi,.

cua

""

,

'

','

,'.~"

,-

.,

,

,

'

'"

tll ba1 h4l1g dQng nJng

hong

s3

:;e ~ t(~'f)z. - tupC-~'f) r.~gian (V,,5) 11. S\! t~ Spa1;1;1i.-tuy

dUn

~~~ai).

(!~ 'hgp he1 cbn~

P.1 -dkg difn"cite

~ (~0!16 b'U~,g h9P ... Chi'. Spas~

li$hl~1IIc~ .,dD cua' phliCm'!;trhm tralmg

the).

- he. cip"'Qai).

te CO d9-Ug quen dlmg han cua

CO dong:

. <111a 1$1iD -bc!t bl~ de Sithr

'

In

{

,

28

cp,c .. .2.. g ,()()

J'

.

' ,Il. ' a2 ... x2{ f ~ l~ ~1~m c~ d1~1'J,lo~l

instanton

cwi me htun trutmg 3uy rQngsiEiu

(V.~) (V.s). @&. Mt blln o~ nghiem lEi nhbm 00). 451 ~~e '(V.S> cbo t~ Iagr~g1anl

I2J(p(-~'f)(lfo/},(V~1)

0".6)

,'~

-,

base 'fv~ t~g diri nm$.

~ :: i:(~CP)~-t~p(-~'f)+&'P~ty-l{f $6 ,t$ bi ~ $.~ ~

"

"

.

1

~An,

~~f

lic} h Db -my d1plg nba

tac vGi ferm1 ~ tll'ClIlg

orl.fide

t!Db cu$ 1;

2S

Coach steu ., 3.- QA"th"n~ ~~2 eo d61 xUngsuperconformal b1. phs va til ph~t nha instantO1J (V.6). tee ld1ao g!a phs va tv phet dol Trong t1~u QlVcnay. thuylt ~ pha trb ~iiS s.t .. ~.

*'

...,

fI>.

(1>'

TbllC bliD pbep dtCb t:"lICtng boa8 1~.

(DC f.(,c) + T(1C) .

.ta

c» ('e>l ...~.

'*- gt~ ~hfit

461 .01 trmm,g 1.1'111

<°1 t!-'C")I°> Ia O. ~e cO '0«11 hinh trttdng

la csu hinh can ~ng dQng l~o h90.

,

Khat h'1~n 11, T (X)

Lagrangian ' "', .. 'Ye do:!. !veri

(V.if> doi vc1i , , be cao

gia

tr~

. £n/ .. cue .,.. (x) Ta tuongtac gs

I

.:t:

. .;::t

;2.' - .

f

c.p . (pC ~

I {--, +2:'~'t'.

a' -(Q1..+,,~)2cp +2.'Pflf}-a1.+,

-..... II (tp~).

(V.n

Cae phtrong trlnh LagX'ange...Elller BUYr* t(z (V..7) :

,

~

.

, (V.S)

D'f/+8,Gi~%.'f'.O

( d.<-+""l-)

trt. CI10 gia oua h~ng b& 80

(1f.;J

f

+;

?1/'-

0

. .

'"t a +)11/ '_.'.".'"

~.,

'8

cae

1-h~ng

ill

tZ'llO'ng boson Va t:rui::t,n;g

0

mo fermion

g1ans .. 1:1"Ongtravng

lUQ'llg 1nstanton

~ cua OIlS boson.

(V..E) doi. vO1 thang

(V.9)

".

.

...

.

~-,-

.'

.. t!'l:tang (V.9)

-

(V.10)

"\.v 1 . =.

gi~)'Ig lUVt'g t& c11$ PhUD'ng trtnb glO:ng Ph1J'Cn).gtr~ olla bosop tropg trinh cOn pb~g ,.. Id1Qrig t}jCt1 glen. ..~ -.. cO .

,

QUa

/( truoong boson ngoa1 ;Jby thu~c J_~' thE' girl chUUJ xao v~ oPo l1&h1e,,: a -,- i 75,~- -. ( Q 2.-+x~) 2-

'.0 spinO' h@:ng. Wgbi~m ::.:ay t~g tlVO'llg

1nst~ton

trong

. , .. d,) y." ~~-x,M -. tro~ - cue 1lIJ£ vOi_de wLon.

.'

, sero '" lit 'fErmion

26

,,,'

.-

nor LUP-

Luf,D an 11$ co ~t

eO dong gOp mC1 ls:n

phocg

v3 cac del x:1ng :c.CD;t~Cn

troog es ha1 trtlCtng hvP:

~Ol x-ing

va,

I. t'! peat.

t~Dg quat va eh~t

cbS cu. 1y thuyat

va

pap them cbo C8C.hi~o bUt glaD mb ~cg chinn xac (ti~m c~) cac vAn d~ ogb1eo ctiu trong lu~c aD giC1. h<}Db ch!mg dDh '~Mt 1118Dgd~c tr1tcg toaD b~c. cae ld!t qoi ch~t

cpe -.5 9~ va dO'!!

.,

.

c~ tllJp cbn c~n pbSico CODdlldng, vb!

1.1

-,

.

. ".. I' .. hi~n d~l, .Ie tdntl !JgttCn. e8Dg tieD c8ng trb Den pbtic t~p va vl~c vOi v~t 1; tbud~~ . cae mO g1SD. v&:t tb,!c ngh1~Dl adD. ~ CUl!gI. V§D.

y cc dDb e~at

~+r:i:l

trong vi~e tl~ kiem me binD I] thuy~t dung dt~

.

(sJc

h1tdcg vi dtJ, ~6 hleh 2 chi3u co fermion cgh1eo::u:.; c, . . ch1tdDg V co chi~u cet giODg vOi qoaD Diem hien 1ai v~ cau true vacuum CU8 11 thuy~t t1tdDg tac ~ch . . dong ll1choc l~cmg t~).

.

.

+

+

+

~

Tuy anieD, vi~e cgbiec c~u cac me blch ~~ g1aD boa ehe etuDE; ta cae g~

-

a

-

, a_, NEfmG CDNGTRIJm OOBG 1JO 00 L1D Q1WI' m LtJp .d

, -

,

cw, 1; UtfC1og 1 - BAt b1An superconforms1 thuyAt dGi xamg - ~ chJ. wft 1,., '

.. chUaD sUo ~.i( 1982). ~

~,

-,..

"..

2 - Cic hf thWfcgi.t!8 cac bemt&fC1nggoan b4i diem cue cac t1'lldngtrong cac SieD 4s tUyGD c~ s1 eu d!51xing m&r{)DgB c 2 - Tfp ell! V~t J.i t B!5 , (1984-).

3- On the

sup8~1eld tormeliem of" extended

superaymmetry. Ir = 2 - Czech. J. Phys- ill (1985

4 ~ A model wi th Spontaneously

) 91'.

rmal eymmetry in superspece J.Phys.

(dS nh~ d!ng).

broken superconfo- - Czech. ,- (2,2) t

5.': n cac s1e'u khons Pen harmonicva cac sieu

..

.,

..

trltC1Dg

, gj,Sl heh

.

h~c elf! b~c

- 'fbong baD ~e

TOngh~ !!P 1m - chi - anb ~~ Dhp cU.ng).

,,1

'-'-.-""'."'

,',

'

N~) : " , ,,;~,. -. , I'

.. r

" ~~.-'

.

+

j

I D/~I HOC I J ~"'! ' I' !1+1\'j;".};{':i" . , \ i , 1..-"---'--'---"

+ - ""'-

o.co;

218

i, ,'J \ ,~..I...JI'.U