As in what recently have you been curious/reading about

God damn gpt...

@TobiasFünke here is an example of a paper i mean journals.aps.org/pra/pdf/10.1103/PhysRevA.54.656

They state the $\langle N \rangle$ in equation (4), but it is rather unexplicit (it is just the series representation of the polylog of order 3)

I think the complexity in obtaining an exact expression for $\langle N \rangle$ is in dealing with the degeneracy factor for each energy level of an anisotropic harmonic well, which is why I think there are no exact expressions.

Also, if you open up pathria & beale (~page 208 in my edition), you find a discussion of BEC in an anisotropic harmonic well and they too split off the ground state contribution to $\langle N \rangle$ and then approximate the rest using an approximate density of states.

also the above paper i guess is treating an isotropic well

i think society and life is going to be unrecognisable a few decades from now

even more so than modern life is unrecognisable compared to 1950s life

it is because of technology

@User198 if you mean e.g. spin operators, then the result is some-times called Jordan-Wigner theorem

@TobiasFünke interesting

is this like some general result about a relationship between hilbert spaces and lie algebras

i thought the relationship was just representation theory

but one needs hermitian representations, so maybe the relationship can get deeper

@User198 and for a finite-dimensional single-particle state, also the CAR/CCR on the corresponding Fock spaces are equivalent (given some mathematical conditions, similar to SvN)

Arai's book on inequivalent representations could be of interest

@Allie Have you not seen a coherent fuller derivation? The "real" system has a dispersion relation that looks like $\omega\propto\left|\sin ka\right|$ that only exists for $k$ between $\pm\dfrac\pi{2a}$ and nowhere else. The Debye continuum approximation is merely equivalent to taking the small $k$ linearisation limit and extrapolating it outwards. This means that, yes, this linearisation limit has to terminate abruptly.

@Allie No, the difference simply doesnt matter. Real world crystals have finite sizes and not infinite sizes.

...I meant CAR (not CCR), because for a finite-dimensional single-particle space, the Fock space is also finite-dimensional for fermions. CCR of course needs infinite-dimensional Hilbert spaces

Does this make any sense to you? If $J\to0$ the field approaches $v$ as it is stated. Of course the first term is zero because $\delta\Gamma/\delta\phi=0$, but then every term of the series is zero if $J=0$ because $J=0\implies\overline{\phi}=v$ and so $\overline{\phi}-v=0$

I mean, okay, if $J=0$ the $N=1$ is zero because of $(12.45)$, but so is every other term of $(12.44)$ because of the $[\overline{\phi}(x_i)-v]$ factors

how can $v=\bar \phi$ and $v=\lim \bar \phi$?

it is confusing to me, but I don't know too much about vertex functions etc. Which book is this from?

@SillyGoose thanks, but I cannot open it right now. My point was that the derivation of the bosonic partition function in the GCE is standard textbook knowledge (as you seem to know?), but not necessarily so in the CE. In any case, I would not expect even for the HO in the GCE an analytical expression for most quantities. But as far as I've understood you, you have one for the chemical potential and or the PF?

perhaps this is of interest:

@TobiasFünke when I wrote that, it is implied by $J=0$. The limit is taken as $J\to0$

@TobiasFünke a set of notes online

@Feynmate no I meant at the very beginning of the chapter

and then after eq. 12.44

is it by K. Cahill? I remember the font lol

or Fradkin

yeah it is also covered in Fradkin's book

@TobiasFünke Oh, you're right; I don't know

yeah the notation is confusing

ah no, that does not make sense I am afraid

i got rid of the hot network questions sidebar and phew it's so much nicer, I should have done it sooner!

Agreed 👍 they generate more heat than light 🕯️

why nicer? :d

I mean it is just at the right hand side, and does not take too much space, no?

But, as they say, some like it hot🔥

> The movie. Banned in China: Upon its original release, Kansas banned the film from being shown in the state, explaining that cross-dressing was "too disturbing for Kansans".

I find it a bit distracting and I seldom care about the topics/questions on there. it seems that for me it got replaced by a list of recent badges and tags as well (?) not sure if they were always there... i don't think I noticed them before

@ACuriousMind Hm. I meant to ask: "Does there exist than some "relation" for finite-dimensional Hilbert spaces, or do they don't have one at all."

@TobiasFünke Ah ok. Thank you.

@qwerty no, I only have watched tags (additionally to the HNQ)

yeah i prefer the recent tags/badges

@User198 without any judging: your questions seem sooo random ^^

1. What do you mean by "know the dimensions"?