| Date set/due |
Exercise |
Comments |
| 8th Sept./
16th Sept.
|
Zee, III.7.1 |
Techincally this is review. We are doing this in preparation for an analogous computation in non-Abelian gauge theory!
Be sure to look at the reading assignments too.This will help, along with the stuff we did in class recently!
|
| 22nd Sept./
7th Oct.
(13th Oct. extension)
|
As discussed in class, complete the computation of the various QCD diagrams to check asymptotic freedom. |
This may be one of the most important computations to have done, if you're going to claim you understant quatum field theory. Bear in mind that this result may get a Nobel Prize one day soon!
It is ok to guide yourself with a text of your choice, but make sure that you actually reproduce every step of the computations! (I was following Ryder and also Peskin, in the class discussion.)
|
| 14th Oct./
21st Oct.
|
Do the exercise Zee, V.3.1, at least by method (a)
Then do the following:
For the model of superconductivity that we studied using a charged boson, write a Lagrangian (up to quartic order in the order parameter) for the low temperature phase, and derive the non-relativistic limit and write the equation of motion. This is the (charged) Gross-Pitaevskii equation. Use m for the microscopic mass and e for the microscopic charge.
Derive the formula for the current density.
Write everything in terms of the variables rho and theta as in chapter III.5
If the current density is the local velocity,v, times the density, what is the relation between v and theta and the applied potential?
Assume that the vorticity (curl of the velocity) of the flow is set by the B field as -eB/m
Hence use Maxwell's equation relating B to the current to derive a differential equation for B which implies the "London penetration depth" and work out its value.
Show that this is the same quantity you would get by evaluating the mass of the gauge field after the Anderson-Higgs effect.
|
The Landau-Ginzburg critical exponents are (althogh experimentally somewhat off) very important in the classical theory of critical phenomena. It is worthwhile taking the time to learn a bit of the history of this subject, if you care. Have a look in various books, such as H. E. Stanley, "Introduction to Phase Transitions and Critical Phenomena", (Oxford).
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
|
| 26th Oct. |
Important!
Make sure that you can do all the work on the in-class soliton handout/worksheet that I gave out today. All of you performed unexpectedly dismally on it, so make sure that you can do it. Find it here.
|
I'm serious. You need to be able to do these simple manipulations....following the lectures like they're a movie is not good enough. |
| 28th Oct. |
Important!
Make sure that you can do all the work on the in-class magnetic monopole (part 1) handout/worksheet that I gave out today. All of you performed unexpectedly dismally on it, so make sure that you can do it. Find it here.
|
See above. |
| 2nd Nov. |
Important!
Make sure that you can do all the work on the in-class magnetic monopole (part 2) handout/worksheet that I gave out today. Find it here.
|
See above. |
| 4th Nov. |
Important!
Make sure that you can do all the work on the in-class magnetic monopole (part 3) handout/worksheet that I gave out today. Find it here.
|
See above. |
| 16th-18th Nov. |
Problems given out during instanton lectures...
This includes the 3 page essay on 'tHooft and the U(1) problem and instantons
Due Thursday 2nd Nov.
|
|
| 23rd Nov. |
Finish studying Zee's discussion of the large N limit once you put in the quartic interaction.
Do problem VII.4.7
Due Thursday 2nd Nov.
|
|