Welcome to Physics 615 : Overview of QFT-

Em , I Yuzloashyau

Text : Peskin S Schroder" An Introduction to QFT "

website : Iep .website → grad . courses

9M ( won relativistic)12

"

÷:÷:÷÷. } "→2

CM : free particle E- = H = I- LU

QI : observables → optsstate of system → 4

pm → ph = - i 2- = - i FZI'

E- → i at 2+2Iat

E- H → Ey - tf -1-42

titty = I 4 free particle2cm

Schiro dinger eq .

tea FM tier- = - - 4- n par et2cm Run

b- = , units L,t,les

t -_ c - i E- L E = YL

@oreut71bnvgeneraliratiouofSehroicliugeveg.7.neteads to inconsistencies ?

QFT solves thru particle creation / annihilationt.seI.Klein - Gordon eg -

E-2- p2 = m2

E=ITEn2 -=

C-aft -a) to -_ map #v states with arbitrary Eco {Iv prob . dens

.can be so I

E- = tofu soI

=

i 2+4 =\=

- or tuna f-

- hou local- time s space as Sy metric

2x ← i2+2.

Dirac ego .

T'- at = ( A- 2x c- Bayt C 2€ t i D 2+72ah - b - = ( aa + pet

T'- at = ( A- 2x c- Bayt Caz ti D 2+72

-

cross - terms 2×2 , 2×22 . . . €2- 2e ) getupA- Bt BA - o

,- - a -

A-1- B' =c2=D2= , } heed 4×4 weak , ee,

cp - i etXe

(A2× eBay c- Caz ti Dat ) y = us f- a )→

apply ( n . . ) afa ' " ( v-2 - 2£ ) f - m2 -1 Cry

(c) ⇒ Ce) bet Ca) # C ')-p2tEku'

A- = c' y'

,D= ij'

, c=ig3 ,D= go

( gray - u ) -1--0see = I X°=t x

'-_ x,thy

gate ×3=Z

→ state , meth arbitrary eco

Causality-

To → I

UCH = < I' I e

- i Ht (⇒

hourelative she 9M E- = PI free part .2

Qu

-i p

✓ = LEI e Tmt I D= jeep Ip> Cpl -# Ted

=Jd3p < al et't 1ps > < Fix .>= '

e- id' calf> =an Irish

✓ = @tTpJd3pe-iEteips.ca .= Thein -⇒%,

Monaro for f I' St - violates causalityIn special relativity-

what if E- = prefer ?

• =@tIpJdspe-itrpEereips.ca -⇒11

" p 1×4 - Idol cos a

4×2×7LT p'd p d ( cosa)

←→P

" =2r.¥⇒ , 1%10 siufplxs-xoije-itph.ieBessel

x >ateicpx - it Fier)

to -0 -

St. please p =

ima JM¥2

o Nti

u - e- - Eee

* .causalityviolated

¥'T' ¥9"

particle

( particle ) x ( anti part ) = 0Causalityis te - e