An Introduction to Quantum Field Theory - Peskin and Schroeder.pdf

P art I
F eynman Diagrams
and
Quan tum Electro dynamics
Chapter
In vitation
P air Pro duction

in e e Annihilation
The main purp ose of P art I of this b o ok is to dev elop the basic calculational
metho d of quan tum
eld theory
the formalism of F eynman diagrams
W e will
then apply this formalism putations in Quan tum Electro dynamics
the
quan tum theory of electrons and photons
Quan tum Electro dynamics
QED
is p erhaps the b est fundamen tal ph ys
ical theory w e ha v e
The theory is form ulated as a set of simple equations
Maxw ell
s equations and the Dirac equation
whose form is essen tially deter
mined b y relativistic in v ariance
The quan tum
mec hanical solutions of these
equations giv e detailed predictions of ic phenomena from macro
scopic distances do wn to regions sev eral h undred times smaller than the pro
ton
F eynman diagrams pro vide for this elegan t theory an equally elegan tpro
cedure for calculation
Imagine a pro cess that can b e carried out b y electrons
and photons
dra w a diagram
and then use the diagram to write the mathe
matical form of the quan tum
mec hanical amplitude for that pro cess to ur
In this
rst part of the book w e will dev elop b oth the theory of QED
and the metho d of F eynman diagrams from the basic principles of quan tum
mec hanics and relativit y
Ev en tually
w e will arriv
eata poin t where w e can
calculate observ able quan tities that are of great in terest in the study of ele
men tary particles
But to reac h our goal of deriving this simple calculational
metho d
w em ust
rst
unfortunately
mak e a serious detour in to formalism
The three c hapters that follo w this one are pletely formal
and
the reader migh tw onder
in the course of this dev elopmen t
where w e are go
ing
W ew ould lik e to partially answ er that question in adv ance b y discussing
the ph ysics of an esp ecially simple QED pro cess
one su
cien tly simple that
man y of