Readings for Physics 230C winter 2012
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Note: The most recent reading appears first.
Please always note the dates.
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Reading for meeting 19            Thursday, Mar. 13

Basic supersymmetry (as if there were such a thing)

Gunion's notes have the most basic physical statement 
that each particle has a superpartner related to it 
by a supersymmetry transformation and that has the 
opposite statistics and is up or down a step of 1/2 
in helicity. For the discussion of coupling unification,
that is sufficient. If you want to go further in a 
finite amount of time, I suggest the following:

Zee's chapter on supersymmetry.
  I've made copies of this and you can get one outside 
  my office door.
Martin, A Supersymmetry Primer
  http://arxiv.org/pdf/hep-ph/9709356.pdf
  
To handle supersymmetry in field theory, a great deal of arcane
and very formal formalism is used. Zee has a short intro. 
You need to be really good with Weyl spinors and dotted 
and undotted indices to follow this in detail. Section 1 
of Martin is worth reading. After that he launches into 
the formalism too. Read more if you feel like it but we 
have no time left to go there. Of course, there are two 
whole courses on this.

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Reading for meeting 18            Thursday, Mar. 8

Gunion IV: 265-279

Coupling unification

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Reading for meeting 17            Tuesday, Mar. 6

Gunion IV: 242-265

This covers two topics: the additional work needed 
to incorporate the effects of scalars and Weyl fermions
in beta functions and some introduction to SU(5) 
as a GUT gauge group. 

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Reading for meeting 16            Thursday, Mar. 1

Gunion IV: 224-227 (beta-function)
Gunion IV: 227-241 (discussion of phenomenology)
P&S: Sec.: 16.7 

At long last, we have the famous calculation of 
asymptotic freedom in non-Abelian gauge theory. 
With all the ingredients already in place, 
it's not too hard to do the last step.
This is a surprising result with major physical 
consequences. The success of the standard model 
hinges on this. It's key to most of what we understand.
The phenomenology in the second part of the Gunion 
reading clearly makes this point.

P&S and Banks 9.10 attempt a physical explanation of the 
counter-intitiive notion of "anti-screening." 
You may or may not think these are helpful. 
One thing to keep in mind is that things 
can look very different in different gauges.
Some physical consequences are described. 

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Reading for meeting 15            Tuesday, Feb. 28

Gunion IV: 210-224
P&S: Sec.: 16.5 

One loop renormalization in non-Abelian gauge theory.
It is not necessary to study both. 
They cover similar material. I suggest starting with 
Gunion. Then if you get stuck on a point, you might 
try P&S to see if it helps.

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Reading for meeting 14            Thursday, Feb. 24

Review Faddeev-Popov lagrangian and Feynman rules
P&S: Subsec.: Relations among counterterms p. 531-533 
Gunion IV: 205-210

The general topic is renormalization of nonabelian 
gauge theories.

You may want to begin by refreshing your memory on 
the material from last quarter on the Fadeev-Popov, 
gauge-fixed lagrangian and the Feynman rules for 
a non-abelian gauge theory. 

All of our sources jump into calculations with little 
orientation. To get some idea on the bigger picture, 
you can look at the P&S subsection mentioned above. 

Then the Gunion reading heads into the calculations 
of the divergent one-loop diagrams.

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Reading for meeting 13            Tuesday, Feb. 22

Gunion IV: 203-204
Gunion IV: 183-186
Banks: Secs. 9.8, 9.9, and 9.10 (if you have it)

I recommend that you read these in the order above. 
The first reading in Gunion connects to our Ward 
identity discussion with a brief comment on how it 
helps with overlapping divergences in two loops.

The second Gunion part is a calculation of the QED 
beta-function and the running of the QED coupling. 

If you have access to T. Banks, Modern Quantum Field Theory, 
you should look at Sections 9.8, 9.9, and 9.10.
Section 9.8 is another discussion of renormalization 
of QED. The approach is a little different, but 
after all our QED work, it should be OK. 
Sec. 9.9 is Banks version of the RG equations for QED. 
Sec. 9.10 is an approach to understanding the physical 
origin of the formal result for the beta-function. 
This becomes most interesting when applied to QCD, 
where the outcome is different and less intuitive.

The pages 187-202 in Gunion, which we are skipping 
for now, are the one-loop calculation of the anomalous 
magnetic moment. This an actual physical result from 
finite part of the one-loop vertex correction and 
is one of the all-time great calculations in QFT. 
I hope that we will return to it after renormalizing QCD.

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Reading for meeting 12            Thursday, Feb. 16

Gunion IV: 153-182 (again)

You will also want to review some material you
probably discussed last quarter, pages 308-312 
of P&S.

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Reading for meeting 11             Tuesday, Feb. 14

Gunion IV: 153-182

QED 1-loop counterterms and renormalization. 
This is a lot of reading that doesn't break up very 
naturally. I think that the best strategy is to read 
through it all once to get the picture of where it 
is going and how the pieces relate without getting 
excessively slowed down by details that are not clear 
on first read. Then on Thursday, we can focus in on 
some of the details more carefully.

The main goal is to get the 1-loop counter terms 
and do the 1-loop renormalization. However, a couple 
important side issues arise.  One is he Ward identity. 
Also there is a little bit of complication resulting 
from the gauge fixing term.

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Reading for meeting 10             Thursday, Feb. 9

Gunion IV: 143-152

First part of discussion of one loop QED.

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Reading for meeting 9             Tuesday, Feb. 7

Gunion IV: 126-142

We now return to gauge theories to see how to do 
the renormalization there. This first section goes 
over power counting to find out what divergences 
we can expect.

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Reading for meeting 8             Thursday, Feb. 2

P&S: 12.1, 12.5, 13.1, 13.2 

For these readings, just try to get the basic ideas
of this different approach to the renormalization group
without getting too bogged down in calculation. 
It is less tied to the machinery of relativist QFT 
and more closely associated with Wilson, scaling laws, 
and critical phenomena.
Also relevant are some of the earlier readings like 
P&S 12.5 and Ch. 8

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Reading for meeting 7             Tuesday, Jan. 31

Gunion IV: p. 104-116
P&S: 12.2, 12.3, 12.5

Continue on the renormalization group.

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Reading for meeting 6             Thursday, Jan. 26

Gunion IV: p. 86-103

First discussion of the renormalization group.

Note the use of beta for two different things. 
The beta(z) of Eq. 201 is _not_ the beta(lambda)
of Eq. 195. The famous "beta function" is the beta 
of Eq. 195, and it is the one that is meant by the 
symbol beta in most of the places it appears.

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Reading for meeting 5             Tuesday, Jan. 24

Gunion IV: p. 72-85 

Here we get the calculation of the one loop self energy.
With that and the one loop four point function, the one 
loop renormalization is done. 

There is more on phi^4 renormalization in 
P&S Secs. 10.2 and 10.5 and Banks Sec. 9.6.   
Also Ch. 10 of Sterman, An Intro to QFT, looks
pretty good. 

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Reading for meeting 4             Thursday, Jan. 19

Gunion IV: end of p. 58 through p. 71 

Recall that the first step of renormalization is 
regularization, i.e. somehow get finite expressions 
to manipulate. To do this, one needs to reduce the
contribution of arbitrarily large momenta in loop 
integrals. The most intuitive methods introduce 
cut-offs in on way or another while staying in four 
dimensional spacetime. An alternative is to reduce 
the dimension of spacetime so that the integration 
measure puts less weight on large momenta. This is 
called dimensional regularization, and it is the 
topic of this reading.

The reading is highly technical and might seem like 
overkill for the problem at hand. In some ways it is. 
However, when one moves on from one loop renormalization 
to the renormalization group and to gauge theories, 
dimensional regularization has advantages.

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Reading for meeting 3             Tuesday, Jan. 17

Gunion IV: p. 39-58

This covers the basics of coupling constant renormalization. 
Then it has a lot under the heading BPH. Most of  
that is really about power counting and counter terms. 
It only mentions in passing the existence of the BPH 
method of proving renormalizability to all orders. 
We will not use this method. The proof from the 
Callan-Zymanzik equations avoids the complexity 
of dealing with overlapping divergences explicitly.

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Reading for meeting 2             Thursday, Jan. 12

Gunion IV: p. 1-38 plus three lines on p 39

This begins the development of the traditional 
approach to renormalization in relativistic QFT.
It goes into detail on wave function renormalization.

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Reading for meeting 1             Tuesday, Jan. 10

P&S: Ch. 8
Gunion IV: p. 1-13

("Gunion IV" refers to Professor Jack Gunion's notes 
on renormalization available here:
http://higgs2.ucdavis.edu/gunion/renormalization.pdf

To get a feeling for some of the issues we will be 
addressing this quarter, take a look at the readings 
above. No doubt, parts of them will seem mysterious 
(or worse). Not to worry. As the quarter goes on 
and we treat them in detail, it will make more sense.

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