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1
Path Integrals in Quantum Mechanics
Path integrals were invented by Feynman (while a graduate student!) as an alternative formulation of quantum mechanics. In quantum eld theory, the path integral
formulation is important for many reasons:
The path int

Correlation Functions and Diagrams
Correlation function of elds are the natural objects to study in the path integral
formulation. They contain the physical information we are interested in (e.g. scattering amplitudes) and have a simple expansion in terms

Observables from Correlation Functions
In this chapter we learn how to compute physical quantities from correlation functions
beyond leading order in the perturbative expansion. We will not discuss ultraviolet
divergences here; this important subject is l

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= s( W? t
Z) We * )W) H fur
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2
Path Integrals and Correlation Functions in
Quantum Field Theory
The generalization from 1-dimensional quantum mechanics to quantum eld theory
is in principle straightforward: we just have more degrees of freedom. To pass from
quantum mechanics to the q

Renormalization
In this chapter we face the ultraviolet divergences that we have found in perturbative
quantum eld theory. These divergences are not simply a technical nuicance to be
disposed of and forgotten. As we will explain, they parameterize the dep

HW 1
1.
(a) We are given the Lagrangian for charged particle of charge e moving through
an EM eld:
1
e
L = m~ 2 e + ~ A T V,
v
v ~
(1)
2
c
~ x
where (~ , t) and A(~ , t) are the scalar and vector potentials, respectively.
x
We see that the Lagrangian has