About Me

When not at work with students, I spend my time in my room either reading, calculating something using pen and paper, or using a computer. I read almost anything: from the pornographic to the profound, although my main interests are mathematics and physics. "When I get a little money I buy books; and if any is left I buy food and clothes." -Erasmus

Thursday, February 17, 2011

Teaching real and imaginary students

I'm currently enrolled in a quantum field theory course, and the textbook that we're using is Mandl and Shaw. I wouldn't be ranting except for one thing-- none of us (is my teacher included?) seem to know what the hell is going on. 

The main problem is prerequisite knowledge: I suspect that none of us have it. Although most of us have taken the postgraduate quantum mechanics course, we only covered non-relativistic quantum mechanics, and did not touch multi-particle systems. So there is a huge gap between what we know and what is expected. I would have thought, for example, that our lecturer would discuss the relevant background  (I would have!) but was sadly mistaken. 

Mandl and Shaw focuses on quantum electrodynamics, and a study of the Dirac equation is definitely needed. I would have appreciated a discussion of the transformation properties of spinors as well as a thoroughgoing work-through of  the properties of gamma matrices. But we skipped that even though it was painfully obvious that our lecturer's thesis advisees had none of the expected background. 

I'm not happy with graduate education (and undergraduate education as well) in my country; there is little reward for good teaching, and so we get what we deserve. Some of the faculty behave as though they were teaching imaginary students-- there is little or no taking into account of the actual raw material. I don't know if this can be changed-- tenure decisions here have more to do with publishing papers in ISI indexed journals (preferably high impact-factor) than with other components of scholarship, such as teaching.

I did accomplish something worthwhile today. I met with one of our undergrads and helped her with the method of steepest descent. Arfken's text contains a sketchy discussion of the method, so I had her work through the steepest descent approximation for the Hankel function of the second kind. 

It's always a pleasure to see students struggle and then reach the needed understanding. In our case, the stumbling block was why choose the specific saddle point -i. So I had her examine the real part of the exponent and track the sign. I then made her show that the contributions to the contour integral go to zero for large values of the  parameter s only when the contour passes through regions where the real part is negative.  We could not use the other saddle point because deforming the contour to make it pass through the  other saddle point i leads to parts of the contour going through regions of positive real part. 

I'll spend the rest of the night being a gammist. Our homework is to calculate the cross-section of Bhabha scattering to first order, assuming the colliding particles are unpolarized. This means trace theorems and gamma matrices. I do have other books and can use them to supply some of the details (Itzykson and zuber's QFT text might come in handy) but feel that it's drudge work. Time to roll up my sleeves. 

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