Recent content by metapuff

1. grad quantum 2. differentiable manifolds 3. geometry in string theory (math department!) 4. grad stat mech 5. grad math methods starting august 24th! psyched.

Say I have a wavefunction that's a superposition of two-particle states: \Psi = \int dk ~f(k) c^{\dagger}_k c^{\dagger}_{-k} | 0 \rangle Here, ##|0\rangle## is the vacuum and ##c^{\dagger}_k c^{\dagger}_{-k} | 0 \rangle## represents a pair of fermions with momenta ##k,-k##. My goal is to solve...

Okay, another question. Let ##\Psi_{0,\downarrow}## be the ground state for spin down electrons (for example we could have a partially polarized electron gas, with ##\Psi_{0,\downarrow}## representing the filled fermi sphere for down-spin electrons). If I try to act on this with the number...

Nice! That's really clever. This seems like a trick that I'll be using a lot. :)

Suppose I have a system of fermions in the ground state ##\Psi_0##. If I operate on this state with the number operator, I get \langle \Psi_0 | c_k^{\dagger} c_k | \Psi_0 \rangle = \frac{1}{e^{(\epsilon_k - \mu)\beta} + 1} which is, of course, the fermi distribution. What if I operate with...

Yay! That's what I'd hoped for, but was afraid there might be some subtlety with spin that I wasn't picking up on. Thanks!

Say I have a hamiltonian with fermion creation / annihilation operators like this: \sum_{k_1,k_2,k_3,k_4} c_{k_1,\uparrow}^{\dagger} c_{k_2,\downarrow}^{\dagger} c_{k_3,\downarrow} c_{k_4,\uparrow} where the k's are momenta and the arrows indicate spin up / spin down. Can I commute operators...

Yeah, Landau can be frustrating sometimes. When I read it the first time I thought he was just showing off, but I think the brevity of explanation there is just the way Russians do things.

Okay, I'm going with the CMT guy. Going to get my ass kicked doing super hard integrals all summer... psyched! Hopefully it'll be character-building.

Like you said, we know for sure that p = 1 (mod 6) or p = 5 (mod 6). If p = 1 (mod 6), then p^2 = 1^2 = 1 (mod 6), and we're done. Else, p = 5 = -1 (mod 6), and so p^2 = (-1)*(-1) = 1 (mod 6). p can't equal 3 mod 6, else it'd be divisible by 3 (like 9), and p wouldn't be prime.

Thanks for the replies! CMT is booming, especially at my school. I was definitely leaning towards the CMT guy, as it looks like he's doing some cool group theory stuff in frustrated magnetism. However, I've written some papers in astro / cosmology and am worried that a switch to CMT might make...

I'm finishing my second year. I've written a paper in astrophysics / cosmology type stuff, and getting a paper out with the hep-ph professor seems like a reasonable expectation. Not sure about the CMT guy though. I'm interested in hep-th because I really like pure math, and want to be able to...

I'd recommend taking a full-on semester course in linear algebra, since its of such OMG importance in physics / engineering.

I want to do hep-th in grad school (like everyone else!). My school doesn't have anyone working in formal hep-th, so I need to take a roundabout track in research (I've been working in cosmology recently). I have two options: work with a well-known prof in CMT (very mathematical) work with a...

No reason not to do 4 years. What's the rush? Your application will be only 75% as good if you apply after only 3 years.