Lecture 1 - February 3rd 2005
February 8, 2005
1
Introduction
The main goal of this course is to develop a physical understanding of what Quantum Field Theory
(QFT) is. It has transformed from being a
Lecture 20 -April 19th 2005
April 25, 2005
1
The quantum eective action for gauge theories
Today we will nish talking about the important properties of QED. If you remember, last time we
showed that t
Lecture 17 -April 12th 2005
April 25, 2005
1
Quantanizing the Gauge Theory
In the previous lecture we found that if the Lagrangian is gauge invariant the PI is simply illdened. The propagator doesnt e
Lecture 15 -March 24th 2005
April 5, 2005
In the case of 4 theory, there is only one coupling , the quartic, and we calculated the RGE
for this coupling. By calculating some physical amplitude and dem
Lecture 16 -April 5th 2005
April 25, 2005
In the last lecture we ended up arguing that the only particles observable at low energies are
spin 0,1/2,1. Today we will begin the discussion of spin-1 part
Lecture 17 -April 7th 2005
April 25, 2005
If we consider a general amplitude with one photon coming in with momentum p and index ,
LI forces,
p M (p, . . .) = 0
(1)
Unitarity informed us that the prop
Lecture 14 -March 22nd 2005
March 22, 2005
1
Renormalization Group Equation - Continued
In the previous lecture we discussed the Wilsonian RGE, which is a consistent way to change the
bare parameters
1
Eective Field Theory
Last time we nished discussing unitarity and our gross conclusion was that given a general Lagrangian with a healthy kinetic term the resulting theory is ne and unitary. Analyzi
Lecture 9 - March 3rd 2005
March 21, 2005
1
Path Integrals vs. Hamiltonians
We have seen that the PI is wonderful for organizing perturbation theory, getting the combinatorics
right and displays symme
1
Renormalization Group Equations
There are dierent points of view on the Renormalization Group ow, but in order to reduce your
confusion lets x our ideas for today. I want you to imagine that I hande
1
Eective Field Theory in 4
Today we will see why short distance physics decouple from long distance physics within the context
of eld theory. We saw it in action for the case of 4 theory. We ended la
Lecture 10 - March 7th 2005
March 21, 2005
Last lecture we found the general structure of the unitarity condition to be of the form,
Mba Mab =
d(LIP S)Mac Mcb
(1)
and we saw that when particles go on
1
Fermions
Lets gure out how to use Fyenman PI for fermionic degrees of freedom, in general number of
dimensions. I will be largely following the treatment found in Polchinskis String Theory textbook.
Lecture 6 - February 23rd 2005
February 24, 2005
Lets consider another example of a simple theory and derive the Feynman rules. This theory
is known as Scalar QED, and it describes the interaction of
Lecture 8 -Marc 1st 2005
March 21, 2005
Lets nish up our discussion of Weyl fermions. We concluded that the Lorentz group is the
same as, SL(2, C)/Z2 and practically this means there is a representati
Lecture 1 - February 3rd 2005
February 8, 2005
1
The Inevitability of Quantum Field Theory - continued
Let us begin with scalar elds, i.e. spin-0 excitations. There is the vacuum state of the theory |
Lecture 5 - February 22nd 2005
February 24, 2005
1
Deriving the Feynman Rules
In the case of a free theory the generating function is,
R 4 4
Z[J]
= ei/2 d xd yJ(x)
Z[0]
(x,y)J(y)
(1)
and the 2-point f
-function and energy.
1
Harmonic Oscillator in NRQM
Last time we saw that amplitudes in QM can be calculated in the form of a PI. We also saw that
doing it in imaginary time you have exactly the same
Lecture 21 -April 12th 2005
April 25, 2005
1
RGEs for QED
As we mentioned last time there are a few logarithmically divergent diagrams in QED as follows,
[g(p, , incoming)e(k, incoming, arrowin)ve(p+k