Rappresentazioni unitarie 2

Piano della lezion-

Caio menino fineCase me = O

Rotenone di Wigner-

IT I Ep ],

r > = A -453 Ip . o > = EIps taps-in -451 por >

xIp ,

r ) per built ! Rw

love I invoice !

= -2 I Fp] Dsl Rw ) : Ipo ' > = E Dslr II lap ,r

' 7Tl rt

ftp.r > = -2 Ds ( Enp ]- '

Mp3 ) :'

lap ,

a >TI

Quest eques.

one richie de che n fort di sometimes . a dye stet

( pot piri ) L ftp.eiyfrr ,ma come

?

O Ipo )I dsp 83 C e - I ) = I = f dat 2e S'

le - 1) = f a8"lP -

S ( p2 - ml ) O Cpo )\ I

Manifesta mate LorentzPARENTE Sl invariance !

-

8 ( p'

- m2 ) = ftp.2-p.p-m/=zLqSlpo-EpltIep8lPotEp ) Ep,

= ftp.Fm2

qpea .

.

-

a he che Elp '- in ) Ocp . I = ftp.slpo- Ee )

dz =

d' '

p 8 ( p'

- m2 ) O Ipo ) Lorentz invariance

L 'espresso sopra e- dengue cycle

alle precedent

84 p - g) ocpo ,=

Elli - Eui ) SCI -11- - -

= 2E± once - q )Slp '

- mi ) Olli ) to Ipo - Ee )

Patent point dire che,

se p '= Ap alene 2E ' or

'( I'

- g' ) = 2E 83 (I - q )

e paws fi fissa la normalization invoiced :

2 (Apj 8'Ve - Nq ) = 2e s' Ck - I ) C pl pi > = 2E 8311¥ . )

che fa n' che Cap lap , > = C pl p' >

In quest mode th Ip > = I Ap > sense reunite di ulterior fact '

OSSERVAZIONE-S.ec/s1pi7--8(p-pl ) ⇒ seethe stat I Ip ) = lap >

Sign. f. cat diT R ( Itp ) = Roly ) Rs IO )-

Dita da Ep ] Swppowano che Ep ] =

R( hi - ' f) ↳ (3)

RCI- p5

'

boost puro

Alena III

p.ir?--ZDsC-Rp5'REp3)IlRpoi)

A

I Rp ] "= RCI → Rp ) ↳ ( 55

' RCI →

RPD"

- I

[ Rp ]- '

REP ] = RCI → Rp ) Lz ( 55' RCI → Rf) HR RCI - f) ↳ (3) RCI -ip5

'

-

Rz

brioche he,

doe che ER, ,Lz ] = O enema [ Ks

,I ]=O

I Rpt- ' Rtp ) = R ! I Ip ,

, ) =[ Dslr )I I Rp,

Rappuoutaaona

Chi spin

Supp .name ore In Ip ) = 12341132101 ↳ (5) =R( Itp ) ↳ (5)allow n

. he

e-

HEI=

Ici, f)

e-iotipcie.ptanion a Ip ,

-7 for

a

e- it F Elp,r > = e

' ill ICI- if ) 513, Ipo > = pickup ) I.to/)5csslp.r7

= Bci → f) I,is , Idk ) Ip .

. > = IF] e- it I por > = e-

ik Ipr >

F

day - I .

II p , , ,

= o I p , r > Rapp mutes .

one di elate

Casom

Siprouder one fine for et ifHeTY ,

. p =D

I guerrini IN ! dee

"

piccolo gmpp" a qua gyp corresponds

?

Si Guidera um Veltre standard ( Eo,

0,

O,

Eo) ⇐ to e we stat Ip.,

. . .

)

http. > ⇒ - I E Ot " B

,= +zeo

3 I e.

= e.

I.

= E. I

A 3

W Ip . > ⇒ - IEM JµB = - I

E' " " Ewe. ⇒Iz EMILE . = Jae .

W '

= E. ( Txt KI ) hi '= co ( Ig - I

. )

→ [ hi ! W'

) - o [ hi,

W " ) =iW ' Iii ,3) = - in

;I I I.

.

Ip .

to

Poto

Algoma are guysE (2) Way → I

.By Wo - W '

→ I

X

5*2*75- view ; im Comin

p2 to =D Iz I > = X I > → in guest case

2=0,

It,

I 2

ma aureus anche I 42,132→ F O

Iarbitzaioi.MIL' two

Gra for il piccolo guy .pe sullo stone standard?

e its W^%. I pay = ?

e-f.) I

.

- ifxh.

- iffy-

e. I pox >

±- if

Si put werehe former di Baker - Campbell

,tenendo 65 che [ Fi,I ] L Fj

e- ice It tibi I

=

eik'. IFe- ice Iz

I pop = e- ie ' Ip .

a > fear ftp.x ) = O

↳alias k IfTry

Po lp.

Si he fear

:Piccologruppo Ip

.

x > = e- it " I pox >

to = ( co

, -0,0 ,E

. ) I f)=12,41132101 ↳ ( s ) Lz (5) (÷ )=(÷! )E - Eoe

'

p = [ p ] C p . ) e I Ip ),

x > ⇐ IPT Ipo,

-Alp ,

x > = IT -45 Ip.> > = tap] I ip5'n- Ipx > = lap

,a > e

- ice " "

"piccolo g wtf

Le traitorous del

"

find guff " Konow wee menein forme Jin wane al

Cen m 70

Son Eastman di Lorentz faut

( Eo,

0,

0

,Eo ) → ( Eo

,o

,o

,Eo ) Corrida . am he mature henbane

area.chef!! ) - al !: ) At

⇒ A = Sla ) Rs C f ) in game ,done 514 = ( I:)

Guianan one [ Np )- '

A Ep ) made to i - to alene inSL C 2,1C )

= S ( Z) Rz l 4 ) S ( z ) corn.

spade alle" troslasiow " in Ek )

DII ( Inp )- '

a Ep ) ) = DII I Sk )Rig) ) =D I Sk ) ) Di:'(Rio ) ) =

= e-

if- DII ( Ski ) Si put mortem che D

'

II ( sus ) =L fr

Esma .ro Dimstnae oh X I l ' eh . ok'

fer une stat generico-

I.I Ip x ) = x Ipx >