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02:55
0
Q: Can we restrict what kinds of identification questions are on topic?

David ZRecently there was a significant discussion about whether a question on the main site should be on topic. I very strongly believe that it is not a good question for the site and should not be on topic here, but the community thought otherwise. That got me thinking about what defines our site's sc...

 
7 hours later…
09:33
Super Yang Mills controls all
'The existence of super Yang-Mills (SYM) theories of a certain number of supersymmetries in a certain dimension of spacetime is linked to the existence of certain cocycles on the super Poincaré Lie algebra' of course it's all cocycles and if you don't know what a cocycle is how could you even begin to understand supersymmetry
"By the year 2015, Maldacena's paper had become the most highly cited paper in high energy physics with over 10,000 citations"
 
1 hour later…
10:43
@bolbteppa You probably know what a cocycle in this context is, it's another way of talking about invariant polynomials on the (super-$\infty$-whatever-)Lie algebra. So what the statement is saying that for a SYM theory to exist that there must be a proper invariant polynomial with which to formulate the action. It's not that obscure an idea :P
 
2 hours later…
12:22
Hmm, so a ferromagnet has a dispersion relation as sin^2(k) and an antiferromagnet has a linear dispersion (abs(sin(k))), in the simplest case. It is strange to me that the dispersion relations differ, does anyone have a nice intuition for it?
 
2 hours later…
14:39
0
Q: Conserved azimuthal generalized momentum = conserved $z$-component of angular moment?

Lopey TallThe Lagrangian for a spherical pendulum of length $l$ is $$ L = (1/2) m l^2 (\dot{\theta}^2 + sin^2(\theta) \dot{\phi}^2) + mg l cos \theta $$ Landau and Lifshitz state, "The coordinate $\phi$ is cyclic, and hence the generalized momentum $p_\phi$, which is the same as the z-component of angular...

Should this question be considered off topic homework (just looking for a calculation), and the answers be considered solutions that should be removed?
14:55
@BioPhysicist I'm not a big fan of the question but I don't think it's closable as HW-like - it asks a specific question about why two quantities that are not prima facie equal are equal. The way to show that might be a calculation, it might be applying intuition, or whatever else, but it's not a request for a computation or a "do this exercise for me". It doesn't show any effort, but that's on its own not closeworthy.
I think the user expects some sort of "obvious" explanation for the equality here because L&L just state it offhandedly, and didn't expect to have to actually compute the two quantities to see that they're equal.
Yeah, I think I feel the same way. Although I did VTC for lack of detail, as they are asking about what they are missing, but they haven't stated what they have tried / what they are thinking.
@BioPhysicist That's why I said I think they didn't expect to have to compute anything - I think they're expecting a one-line answer. Some people don't expect books to state anything with a non-trivial explanation (like an explicit computation) without giving that explanation.
So "What am I missing?" is their way to ask "Why is this obvious?", to which the answer is "It isn't" :P
15:13
Very true haha. How have things been for you lately?
Uh..."pleasantly uneventful" I guess is the best way to describe it? :D
Haha sounds like something I would enjoy
I had two weeks off from work that were originally intended for a trip to Sweden but we didn't go (for hopefully obvious reasons :P) so I just spent the time occasionally meeting friends and playing video games. Now I'm back to work but it's still from home but there isn't much going on there either because many other people are also on vacation so that's nice too.
What were you intending to do in Sweden?
Sounds pleasantly uneventful then haha
15:21
@B.Brekke look around Stockholm for a few days, spend a week on Gotland while their annual medieval festival is ongoing, then travel back via train and stop for a day in Lindgren's home town. I think we had two or three days in the itinerary left where we weren't sure where to go when we stopped planning and decided we wouldn't go
16:04
@ACuriousMind now it's a pecan pit ;-;
@ACuriousMind I guess that led to the present day where I'm putting in a constant effort to prevent this animal from killing itself
16:53
what does the abbreviation "cf" mean?
@satan29 'confer'
ah
thanks.
 
1 hour later…
17:59
I see that time travelling chess thing a lot around lately and it seems to me people have already forgotten that there was a time travelling RTS which came out years ago
Nobody weeps for Achron
 
1 hour later…
user434058
19:03
Is is legal to alternatively write the E-L equations for the Lagrangian as: $$\frac{\mathrm d \dot L}{\mathrm d \dot q_j}=\frac{\mathrm d L}{\mathrm d q_j}$$
user434058
In other words, is it legal to commute the partial derivative with respect to $\dot q_j$ and the total derivative with respect to time?
user434058
@FakeMod I am sorry, those \mathrm d's should have been \partial derivatives.
user434058
I encountered this swapping while going through the derivation of Lagrangian formalism from D'Alembert's principle in the following form: $$\frac{\mathrm d}{\mathrm dt}\left(\frac{\partial \mathbf r_i}{\partial q_j}\right)=\frac{\partial \dot{\mathbf v}_i}{\partial q_j}$$
user434058
So I wondered whether this could be done in the final E-L equations as well.
user434058
Moreover, is the above "swapping" trivial/obvious, or is it true only under specific conditions (of course, the functions need to be sufficiently smooth, but are there any other conditions which need to be followed as well?)?
user434058
19:20
I have tested and tried some trivial cases, and in them the following equations $$\frac{\partial \dot L}{\partial \dot q_j}=\frac{\partial L}{\partial q_j}$$ seem to produce the same EOMs as the standard E-L equations. So, assuming it is true, why don't we write the E-L equations in this alternative way? To me, the alternative way seems way more symmetrical (thus beautiful and elegant), and also more concise (so yeah, aesthetically better).
user434058
20:37
Anyways, 'night!
20:54
In classical Hamiltonian mechanics, does the algebra formed from the observable functions on phase space and the Poisson bracket correspond to the algebra of some group?
I have seen no reference to anything of the sort so I was just curious
@Charlie it's infinite-dimensional so the question is a bit subtle
but the simplest answer is that the corresponding group is the group of symplectomorphisms, which may or may not be what you know as "canonical transformations"
(annoyingly, there are several inequivalent uses of "canonical transformation" in Hamiltonian physics)
@FakeMod No, because the Lagrangian is not a function of time.
(well, it is in "explicitly time-dependent systems", but in the contexts where you have partial derivatives w.r.t. $q$ and $\dot{q}$, there isn't such a thing as $\dot{L}$.
I have to refer you again to this answer of mine about what the L/H are functions of in what context :P
What do we mean by "Hamiltonian symplectomorphisms"?
@Charlie Scroll up
(on the Wiki page that is)
ah lol ty
21:10
(you might notice that it's kind of tautological to say that the group of Hamiltonian symplectomorphisms is the group corresponding to the observables, but that's math for you and in the usual $\mathbb{R}^n$ situations it's a distinction without a difference anyway)

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