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, outgoing, arrowout)|e(p+k, incoming, arrowin)ve(k, ou
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 the amplitude of the theory satised all the properties 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 exist and there is no way to make sense of any amplitude
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 demanding it to be independent of
the cuto we easily arriv
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 particles. As a start it is simplest to
consider the famili
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 propagator must have the form,
squiggly =
i
p2
+
cp p
p2
(
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 of the theory with the cuto. In the case of 4 theory we
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. Analyzing the theory,
within the perturbation expansion, we cu
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 symmetries conspicuously. Why wont we just always start with
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 handed to you some theory, with
all its parameters, coupling
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 last time by introducing
the RGE for the parameters 0 and
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 shell the imaginary part of the propagator gives us a f
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.
Lets start with the most basic fermionic system, with
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 a complex scalar eld with light. The
Lagrangian is,
1
1
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 representation of the Lorentz group acting on a 2-dimensional space
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 |0
and there are states with one, two or more momenta |p
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 function is simply the propagator,
(i)2
2Z
= i (x, y)
JJ
-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 sort of integration over all paths but the
weighting fu
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 tool in High-Energy Physics (HEP) into a unifying
form