Things I should look at before I take QFT?

1. May 12, 2014

wotanub

I think my weakest area is things like integration techniques, complex analysis, and integral transforms, but after a few google searches I can't really find what makes QFT so hard when people see it the first time.

I really don't understand how to evaluate path integrals or those n-dimensional partition functions or how they're related. The infinite sums baffle me in the ising model things.

Anyone have any reference for making sure my math skills are adequate before I get lost next semester? I really want to get a handle on working with fields, both quantum and classical.

2. May 12, 2014

ZombieFeynman

Wotanub, what's your overall background so far?

3. May 12, 2014

wotanub

I just finished my first year in a doctoral program. QM, E&M and SM.

I've done some undergraduate abstract math.

4. May 12, 2014

ZombieFeynman

The second year of grad school is a pretty common time to take QFT. I think you should do fine. My favorite book is Altland and Simons Condensed Matter Field Theory, but perhaps I'm biased. You should look at Student Friendly Quantum Field Theory by Klauber, which is very new. Some people like Zee's book as well, though I think it's better used after you have seen many things for the first time. Peskin and Schroeder is of course a classic, though I am not a fan.

5. May 12, 2014

WannabeNewton

Do you know how to find residues when doing contour integration and use things like Jordan's lemma? Are you comfortable with readily taking Fourier transforms, particularly of things like the Dirac delta function? Also how adept are you at computing Gaussian integrals e.g. using the method of completing the square?

On a different front, how comfortable are you with infinitesimal transformations and their relations to Hermitian generators of unitary transformations from QM? Finally do you happen to know any basic representation theory of Lie algebras and Lie groups?

6. May 12, 2014

wotanub

No.

Yes, I know the basics.

I know how to do the one dimensional ones, but the generalizations are confusing.

This:
$\int \mathscr{D}[\phi(x)] \mathrm{e}^{-\beta \int \mathrm{d}^{n} x(\frac{K}{2}(\nabla\phi)^{2}+\frac{t}{2}\phi^{2}+u\phi^{4} - h\phi)}$

I don't know.

I think I need some advanced integration practice or something.

7. May 12, 2014

ZombieFeynman

You need to get familiar with contour integration.

8. May 12, 2014

Staff Emeritus
+1 on the contour integration. Matrix algebra will also be helpful if they have you proving a bunch of trace theorems.

9. May 14, 2014

wotanub

I've found a great reference for posterity. Physical Mathematics by Cahill.

It presents topics in a succinct manner, then throws you into exercises. Every chapter could easily be read in less than a day and the exercises finished in a day or two. It has all those "little" things needed to fill in the gaps. He doesn't go into great detail on any on the many topics, but it's a good reference for establishing familiarity.

It's not "tell me everything about path integrals" it's "what is a path integral, and tell me how to do them in as few words as possible." To put in perspective, the path integral chapter is 38 pages. The following RG chapter is 12 pages.