the :ions abdus salam - International Centre for...

theabdus salam:ions

educational, scientific

££££ international centre for theoretical physics

international atomicenergy agency

SMR.1320 - 4

SUMMER SCHOOLon

LOW-DIMENSIONAL QUANTUM SYSTEMS:Theory and Experiment

(16 - 27 JULY 2001)

PLUS

PRE-TUTORIAL SESSIONS(11 - 13 JULY 2001)

FORM FACTORS AND CORRELATION FUNCTIONSIN LOW-DIMENSIONAL QFTs

G. MUSSARDOS.I.S.S.A.

International School for Advanced StudiesVia Beirut 2-434123 Trieste

Italy

These are preliminary lecture notes, intended only for distribution to participants

strada costiera, I I - 34014 trieste italy - tel. +39 04022401 I I fax +39 040224163 - [email protected] - www.ictp.trieste.it

Co-Uu (oji

\U -Co^o

- o-

1C~£ School

LA* OU

LOU

7a 0

°f

JT

f

fOt

JIM CJU COO Of

7^ of

t>Lfy>

bo

c \ 4

j \ ' €

flit o\

ft*

/M

\

- \ T;

Uou cU

/ \ K

ly

L

us>

g,\ U

PA O ^ ,

to

r \

I

M>\

fXVtAt CJiA CUU

JUAX>Z< -CQUXkJ

app

75~O cum

cd -ft CoUsU <

'GO

oc>u*-cc*s< o[ <d*4pCbuOM i^tX>Zu

\

fo

CLud Tbu CX>U^^^MCL of.

patAUnhoj j y • o

5'.

AUoufd. h*. &c* pit CLto teal S-

" UZi PI

dvt (y itex> AAAS &U>A topic. .A*UA CMtots 04 Q /af-c-^i uc/ ,'cixs

Of Ttu $ - <UJ cjal* QA d ^LuUU^CU £>f

j

KU fGO

,\ OA AJiLupU fiA p*> ; w <

f

M-tOM ttctJ<

U<>

jJuuCLX, be

hoc

' ' exy

p

?(,

Mjih\<tA\ •eytlttLce-cCCy-. hosu2o d Q 4-/UTZ^C?

5-

IP AUJ he

C\ LCkC

•j-

LOtou To

t L u AAI>[ *i Cuts

/

?wo

€{ f 7J 7

7^

U/

.U. CJTV X-

u f

pu>j UM < r Tiu

^ ^ _

^ .

tcO&u CC/

X QPPWQ Ui Caiu/ l

d o f

"*<* L{

/

v)Mt/u of:

UA

\A)>

Cuapt ofof CK^l' {o <tu^o 7,'

Tootc*

< > CQ*J (

fvuucjf: ca of.

JUUQJU

Guuf d

' 0To

o[

\U

TO Tul-u k Ttu ApG U. of QFT'-y

ouj of.

f

*uJ 7;. ojxy

CO<*

QjUU^L>i'

f Cf \

CUL, d cutoff A f wiSu

/Q O iCLU .. t'oUJof

•fox iuMQUU

CO -I

lU^eIlLA CX>U cL< '"< C\U

2-

\Lu -ff-ttd^ c^tu oOQA Q tAisu/*. cl by [k^*L AtciMctf

1/

6 ~4 \

C fTu< vtUi.c of Tto,

of

\A

JI CCLJ

-)(?.

QJU Ao -

/H<: / . . . p.- I

z / . , .

*• S.

y y

Z 16

O 1

'go

y O(O

V 2.

to to

tO to

-u-

'- f z I

OXA r>

O f.

couft t/4A cuu .oif cu^M d i^a CPU (OLUSGJ

H(f - O

zUfL

CQJU •CJOJJ. ( iiu /us of - i l -

pVUCUQtA V.-c

A <

\JU of

(Vox H.H

W< CXUA u / * out of f^UCUr b

CUx d Qp CuuJCLQp CuuJCLy

- A -f-

f "lUs j 3 -

\\MAAA A

0

q foetus. fuJ

-o-

CUU- Q

Ay^tou To OLu o{ Tec,

V(A

Jt A.

>M

H covu^ou^ Indeed To <5 f

d

*

€e

- V <UJt),

Tut

cfi-

Itoi

I

y U.Qpp-cci

{. e

A* t UJCCJ, OO - 15-

ou

/ ' • < ? > CUJCL (OU f /

\o ct // COj

JLU taJ7iyCU

be

oufi

S: vc <.*cut,eh ocut,ef Tut* ki^a at

\\XJ('-

tic'

5**

yo \

A nt C

tu

ft-

-b k-c ecu•f>.tt'<*4

C&J r>o

/ . / .

- 17-

JT r<\ ohvicuA AUJCIA if w* MJ<xk( a f,"uj~

L u tur.d. To

J.JU LJUO

7C>

oOhcoJ:

- > CO

ZM<JU>

fA 4 f

ty t<\ C/>10

iCUty

'y

'

f >- /

pot. \

U

a

ffeW A

c{ Tu, {;x >

T ,

. „..V

y

ux Tuj

1lUfy

- &

'

- Of

9Jy\3€

= 1 - - IL

ifi-i)^ -0 /

- r

i

oorsutcJiou. -ZLUrtU W . ' V ^ GUJ y

fo

/

^ ftu

I'T i^ GUuOayA povUbU ^o .cou*idc«-

«

fs£oxA COJSKJ O<^ O^d y), UcuJc

B 3

2

f yJt^u) . J o

COUI tl CAM Vcuucu*: o I <CC& (Us <COLO('\JC<SH£lM V V

Of

7*

To

\o lit/y

Pun utt UCUJ*..lU"

OGUCL*JaJf<

tovu

O<J Of

of

<r

/ f

deo>T v-- cut

2u

JT

up

I

7< -

f

L

Jo lU>*tt<&;oAf Guts ot

« > •

ilA Co usJi dtsuQst, 'ptt

l-Ol lf

Q Sirt S-f

] - zs-

9 7. - 9 0S- I

~\U-LAl cM<VUf><A. lUse/f

of.

p

OJtA CQMJI p ! y

CAJ U<'M QM

c XUJ

u*>

A let hit

s' = s '

body

OV Ct

p /'t' TL<d<^l

'tUt TUt

lia - body {«* cf •'<><, cf. Tu,

><~CA

s* . / Lu cuu

Zl

CJU

a

p -z.\ o

f

lo,

• t

I X

l<>(•

-zt-

r

**JU*

/

S' - 7T x <• )•

1U -f V ' x

Q\ Ttc/ >> AA

A M

c 4

abl< ^

r (,-cA H

/AA U Cod- ISh 4 S

\AZAJU

o f cl

c

A UM ; 0'UUf

f

c

/I ->

f

UA CJXJL^i

GO

- *\- x

K--0

z

Co

•13 - i / r . « ? I J

'"A ,&A<

QQ

- 35-

1 -PO j P

0 J—

f - i

U><

—>

CO

0

p*MU q xq

X

luj U 6L\

o x

Pout* Ta

Oun

ecu

ouut

/T) )< of Tiu

5' *

^ V

l', a COCtSti<JJLAQ_J,'o<C4

4

Jf

su*u & -

O

-S 7

\1>JO JULXJO

tU(

3

7 *Uy t /GUU *Uy t / c Co t/o

/ >i

d

s1

$ - A-aeuc-t* QjL/d TU* 4.Y-GICJ

To d<Zvouul UJ f

A (

t\/OtU t \

Of

(7 '

f

Fo

\JUUP

COM M)~U7/

i

<O\ oM

CO

iu

p

/

t ( ot

btpi^kf

n ^ <?/

do

Jy CU tUjl O LAO t

Z^SUl Of.I /

<D

COtLc^i dot ILU / O

\\A< Q

Af

eK? («*7

Zftt{f

RH - Z

/

H -

R

/? ^

Itlt

H

V I f

y

CU, 7 ^

7 -

Q rpolMlrp

(nS

= ZA/

<t

fu/tec"''/

V Cr

oa

y /y (x_t *

f C(ctp

r e.

7i

(.

f

Co-U

C-

C • -

M

c/2

GO

c =•

d/

. ^ (

(It

4~t

2f,

k 'o u <

(LUO -

°t45-

lu n

CO

U-uu

QokiUAA

y

of'

7

I

- 2L-COi-CfZ4.hu

cM f

$

'7

s

ffiu?;- SCUt

4

. 64/3

OSJU &

OO ZSU CJ,' O

7a/

U-

2j

:

I

1 /

GU

0.14

0.12

• 0 . 1

0.08

0.06 -

0.04 -

0.02 -

10 15 20 25

. 3 /fSS

3 0

\O

V

Figure 14

Vaoicz OzJcu

f /<•" tU^cny f CLL<

f

j(7 " .

of. Tu<

~\vu eutA oJy

U 4 * | . •

Hurt <JOVU*A.OU — — ~> fr~ •«* < ^ > - ' / j V - f l U )

S-

£ ~ AM

1 JUS

cd

icJcieS.' f/«cl

x^u;

jrf. co

o(*o*Jcvz

£ Tux

ouP

f

1-

- 51'

6

\/s. /. y, s. s _ 7*

\JOOJUJ

-

<Cf

a

hY

s -cd"

c d

o[

cdr

tA ^ y

; r a

OUA

Ziu* -

ecu

- f

M

f (jm t 2cu

01 \u fV

F

lieu a

O

-54-

2/ri 61 \

6q

'/

Alt

7

(SI?

A

?'- "7-J:

Foz

€ X p

tU 7

r. A/

a?

12 ] 7Z

/ /t p

Z

<7

2U'O

Tu/

CO

= 77

cow

itM aa

'

f I< C-

-S -/ 0

-V— - I

•llu~ S7

A

-a Z. Cx>\ ft Q

.3 -y-<2>

«

V V>—

Uu ff

t

•'J

ULUOb

P..7

/3

fou T itaA To ef<'o<o

.

f LLUpo-Co\p

o/

o <U

O O-UA i<o< FF occu-z

P

ByXAJCLJ<C& 7LOO- -.Mody

y

•Si-

u 4

a ?aA^coU<vt

3 -V .V C

= re

c

i' caM y

/ •

r.

v

k\ -lo-

cuu p p

A oou I U* 7U.CS?

f.

Ht/c*,

_ / &AUA ( f

3 -

i - e 7f' - I

Q - . . <?

\

p

v

Ncuu-tUy , '

y A

y \Ujju FA °^ ClAyAotp.o 7,'exit

d by ^Lu • CUJJOAAJOJ-O UA <&*'<L*S 4^o^ o (-{

<A

->

OMJ,

\

*.V

CXUJ be Aecu QA UAU(T of 7LU

1 u (3D

(•Q'\9~- Q 9'S ~ F (9 — Q 9 9- 'T'

f,-c

[ Q ^ . M » f * ! \A f L** I'l *-* ' t> V "fc^

UK

At

9

27,7: F

Iti'-f.

S' b

U)l 10

9

it

&

QMQ — <*,• ^

.+ - J H -

'it

4(F

X- Q -

I / .

>

7TI - I

f I3

I

F

Q" FF oi' 7

'

e^yvi ffy7

O f.

lu *JO - ho&y o6<cuc*t-e^iy ^

OJU cocao

T? U U)

euuy o>* f,' c

7 po

Id

l OcJ

 " •

Tlu

OJJ o<C(

rr

Hi

^&•

l-\VU

Pox

4UUp0

Ho

cUjoUutuioit o[ Tut

f

zo 1

7<f

0

>z

/ \

•400.0 , 1

I r1 2

O"\UAA

f (i\

f

fo

CU

- A

Z 3

a ]

X- £O -Coio r lieu

&OUJVCU(4UJ u)ocyA- To -Cook cu tT

ocu c^ c\tA(JU'& (*

tr 2 ft Z

Tu'v.'a/

Cuud S • -

M0

". -e ,a

fc llOvOi 'LLf \Aji •£/

r>ot

d

W/

M

'u? Co tu FT

pJUUU.U

f = All

0 =: 2n z:z:

~ O

pucsi CotJLAA At

iLu

o[ TtxU MUM - -tooowy r^C/C(/U>^ JPc' v-°Of ^Y

• • • • ' • • • • • • • ' • ' 6 • • •

" f lu OOTJu t'A p.I Met*t'A p

z /<r ^r,

- AM - k

OS

c 3

3 2

U

F

oo

* "

z^ c

7T ^ ^ > ni

2

'-Au.tcll

-f s T

V.

"J- UA 7 <u, K

by

)

Go S

— 2

V

r e

7 V » d ;

Uf f' f

^ O f

a

10

QO

2n •=

JO \?

Cum

aA .

7i // 3 \

6= / ! - 1

-- "

?

<2 <^

h<

'U K -f X.

vu.

oii LA.

pI

y ,'cf

,v ia ot

M hy J>

7T

X + f r- . X

< X' 2

*^oTa/ 01 diet of cf

J.C, /<

-CM ( p

a

A1

n /3

Ct,<AjoJ<€>2

I 'A CXMO CAGUA d QM O

Of I Ux Af>Q,C< of

\A)l f

- t

<J w Tut %; pe^ J

allI

AtoJcm oyviAJCiA^ Tu^ ToTcU oidit* c(_

^ / / 7

M

QAA

6*

I I .; < (7 ~

L* TtOC<

M

felt iUA C&^ZU^CXJ of 7bu A^teCi •t'uc^tcu^t' hy

OAJUL

\A<=UO<L ^U e ^ i • .jo ((o LJ i

~ I

= 3

Me

54

QAAC ^ ' ^ o// 9

6OVU Apo^cLqM U UJ* Itf lLu< <-OU{j>o<U U

-^4jccewoa<\ ct/u.

*\\JU

Q /k} r, dj ft (k)

HJ "i

x

O

^ fn

6CU/

CLU

n - l

VI"-I

odd f <'c/^y QJU

" J

' 7'

X + X

cluoU of. 7iu

r

(Lu \

= 2, d

B

Qo

0

the :ions abdus salam - International Centre for...

Documents

Transcript of the :ions abdus salam - International Centre for...