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1:32 AM
Q: References on mathematical stacks for a string theory student

Ramiro Hum-SahThis question was posted on mathoverflow (here) without too much success. I'm hoping to read the famous Kapustin-Witten Paper "Electric-magnetic duality and the geometric Langlands program" and the related "The Yang-Mills equations over Riemann surfaces". The following statement serves to explain...

1 hour later…
2:34 AM
@Slereah yeah, the "packets" terminology and popular depictions of photon energy kinda make it seem like even a free photon must have energy a multiple of some "lowest-energy packet"
2 hours later…
4:11 AM
Please tell me a proper stack exchange for the use of ideal gas equation in real life
2 hours later…
5:47 AM
@PrateekMourya It depends what you mean by "in real life". The thermodynamics of non-ideal (i.e. "real") gases is on topic in the physics SE.
@JohnRennie I see his point though, don't "use in real-life" questions tend to be closed as off-topic?
The derivation of ideal gases uses so many approximation so i want to see if it is any useful ii n real life
In real life the ideal gas approximation is surprisingly good.
You only see non-ideal behaviour at very low temperatures (i.e. -100°C) or very high pressures (i.e. 100 atm)
Does it work on high altitude
Like planes
5:56 AM
Thanks now i can easily digest this chapter
2 hours later…
8:16 AM
8:35 AM
$\hat{\mathbf{H}}(t) = \mathbf{U}^\dagger\hat{\mathbf{H}}_0 \mathbf{U}$ where $H$ is the Hamiltonian and $U$ is the time evolution operator. Since the two operators commute, it can be shown that $\hat{\mathbf{H}}(t) = \hat{\mathbf{H}}_0$. But we do have time dependent Hamiltonians, right?
8:46 AM
It's basically the condition of conservation of energy
Which requires time translation symmetry
9:13 AM
Hi GooD MoRninG....
Are the two statements "a closed system evolves in accordance with Schrodinger's equation" and "a closed system evolves unitarily" equivalent?
@Yashas not really - how would "it evolves unitarily" tell you that the system obeys the Schrödinger equation and not some other equation whose solution is a unitary evolution?
@ACuriousMind I can derive SE with this assumption: $\mathbf{U} = \mathbf{I} - \frac{i}{\hbar}\hat{\mathbf{H}}$. Except for the constants, the assumption can be arrived at with some reasoning like probability must be conserved and time evolution should allow composition.
@Yashas The equation is wrong (that is the infinitesimal approximation to time evolution, the actual $U$ is not equal to the r.h.s., the r.h.s. isn't even unitary) and I don't see what it has to do with my point anyway.
Yes but can't I can take the limiting case with a summation of small $dt$ which would give $\frac{dU}{dt}$? I am not sure if I have done some mathematical nonsense but I somehow get SE from the limit.
9:25 AM
"Time evolution is unitary" reasonably can lead us to believing that there is an infinitesimal generator of time evolution (via Stone's theorem)
it alone cannot tell us that that generator should be the Hamiltonian
i.e. $\partial_t \psi = A \psi$ for some operator $A$ is what you get from "time evolution is unitary". That $A$ is the Hamiltonian (times some constants) is additional information
alas, if you're not thinking about quantization then there's no content in saying "the Hamiltonian", so then there's really no difference between "the Schrödinger equation" and the generic notion that there is an infinitesimal general of time evolution
Ok, makes sense. They are not equivalent and require more assumptions to be made about the choice of $A$.
does an infinitesimal general lead an infinitesimal army? :P
Does anyone know Next.js?
2 hours later…
11:04 AM
What am I supposed to flag a question as if someone re-asks a closed question?
@NiharKarve vote to close it as a duplicate. What's the question? I can close it as a duplicate if it has a tag I have a gold badge in.
11:34 AM
@JohnRennie This one is just a repost of their previous closed question. I wasn't sure whether to flag it as a duplicate since it says to do so if "This question has been asked before and already has an answer" (which the duplicate question doesn't)
@NiharKarve edit the tags and add the quantum-mechanics tag. Then I'll be able to close it as a duplicate.
@JohnRennie should I really? I'm not at 2,000 yet so it'll be added to the edit queue anyway
@NiharKarve yes, add the tag. Hopefully someone else will be along to approve the edit. If I addthe tag the system won't then let me close the question.
sure thing
@JohnRennie All right, it's been accepted
@NiharKarve Closed! :-)
11:43 AM
Very nice :D
2 hours later…
1:42 PM
Would it be possible to analyze exponential graphs using calculus, different series(such as Laplace transform etc) and in case you wanted to know, I am doing newton’s law of cooling.
Calculus does work on exponential functions, is that what you're asking?
Yes but the idea is that I deriving the equation of newton’s law of cooling but my high school teacher said that it will be a bit easy to derive an equation that could easily be found online so therefore I am thinking of how to make my report a bit more difficult by adding more analysis. Would it be possible? (Any help from you would be very useful.
Well, I'm not sure how much extra "analysis" you could do on the law of cooling itself, it's not a particularly interesting equation, in that a graph of "rate of cooling" against any of the input variables would just be a straight line
You could look at the Biot number, that's written just under it on Wikipedia, might give you something more to talk about
@Charlie it's possible that they need to set up a differential equation in temperature
Because heat transfer causes a change in temperature
Would it be possible to use Laplace transform?
1:56 PM
so you end up with $t' = k(t - t_{env})$
@GeneralMO7 Possible, yes
Overkill? Maybe.
Oh I see but do you think it is a good idea for investigating overkill?
and thanks for the equation
and what other series or something that might be a bit difficult for a high school student?(such as Taylor series, la place transform, etc)
Maybe sorry for not being clear but in general can you think of any other application when analyzing the graph?
2 hours later…
3:35 PM
Hey everyone!
I just asked my "to-be thesis advisor" for an interesting subject, and he said yes!
he said no?
Hahaha he did say yes
He proposed something on AdS/CFT and I'm really happy about his proposal
I'm trying to figure out what the /s applies to :D
3:39 PM
It was referring to the marriage-like phrasing
4:10 PM
@GeneralMO7 again, using a sledgehammer of a Laplace transform etc. is unlikely to either simplify or illuminate solving a linear first-order ODE
although you could make it slightly more exciting by dealing with a body of changing surface area, i.e. by giving $k$ time-dependence
4:42 PM
Q: What to do if I come to know the answer later after asking my question?

ultralegend5385In this question, after getting a few answers and some discussion (which honestly didn't make what I needed), I myself came to know the answer from a book. What should I do? Delete it, or answer it myself?

2 hours later…
6:14 PM
Whoa, a new ACuriousMind profile picture
4 hours later…
9:45 PM
> Iran's most senior nuclear scientist Mohsen Fakhrizadeh has been assassinated near the capital Tehran, the country's defence ministry has confirmed.
A sad day for nuclear science.
@ZeroTheHero I will ask the user to be more specific. Is there anything specifically that needs to be explained in more detail? I'm trying to help clean up the unanswered queue. This is the question:
Q: What does it mean to assign group operations to distinct sets for space groups?

B. BrekkeI am trying to understand space groups in crystallography. In International tables for crystallography, for a nonsymmorphic space group, they list some symmetry operations. 8 of them are listed under the (0,0,0)+ set and 8 in the (1/2, 1/2, 1/2)+ set. What does this mean? Are there 16 operations ...

1 hour later…
11:15 PM
I'm finding scarce information online talking about this, is it abuse of notation to raise and lower the indices on the Lorentz transformation matrices? I.e. $${\Lambda^\alpha}_\beta g_{\alpha\gamma}\overset{?}{=}{\Lambda}_{\alpha\gamma}$$
I feel like they aren't tensors and so the answer is yes, but I have seen this done a few times in (what I would consider) fairly reputable sources

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