 6:05 AM
Are there any techniques to decompose tensor products of SO(8) / Spin(8) reps by hand? 6:30 AM
I can barely do it for $\mathrm{SU}(2)$ 6:55 AM
@NiharKarve is chapter 8 of this any help that does give the dimensions nicely
but I don't think the Young tableaux work in general for the non-SU(n)'s
ah well
LieART it is That chapter has some discussion of $\mathrm{SO}(n)$ stuff and an $\mathrm{SO}(6)$ example (and a $\mathrm{SO}(5)$ example) which might be of some help
There's also this, appendix has stuff on $\mathrm{SO}(8)$ 7:37 AM
A weird question, but in a battery, the anode electrons want to go to the cathode, but there's the electrolyte that's keeping them from connecting. When connecting a wire, doesn't that make the electrons go further from the cathode, therefore decreasing electric potential energy? 7:49 AM
@JingleBells I'm not sure what you mean - in a non-ideal wire with finite resistance, there is an electric field in the wire (according to the voltage gradient implied by Ohm's law), and the charges in the wire just move as dictated by that electric field.   Is V2 significantly less than V1 not due to wire resistance, but due to the bigger distance between the electrons and + of battery Ohm's law is $V=RI$. $I$ is the same everywhere in the wire, $R$ is proportional to the length of the wire, so the longer the section of wire, the greater the voltage between its two end points
alas, you're measuring the voltage difference strangely - you should think about the + and the - pole of the battery being infinitely far apart for the purposes of analyzing circuits
they're isolated from each other - it is only through the wire that the electrons at one end can "see" the potential at the other end My reasoning is that since electrons in - want to go to +, they have to go thru the wire path, but as the electrons get away from the +, the distance between the electrons and + increases and therefore the electric force that pulls them together weakens. I'm wondering how do the electrons even go away from the +. I know I'm thinking about it wrong, but I'm just imagining an electron and a proton at some distance apart wanting to get closer.
How do the protons in + manage to attract - thru the wire? Aren't electrons supposed to just stick to the electrolyte wanting to connect to the +, cuz after all that is the shortest distance and the attractive force should be highest. 8:25 AM
@JingleBells if you want to really understand how batteries work, then you need to go read about electrochemical cells
it's not really so simple that one side would have "extra electrons" and there's just a straightforward electric field/voltage between them

3 hours later… 11:39 AM
@ACuriousMind While you're playing good video games here I am, looking at the bottom of the barrel for adventure games
I've played all the good ones too many times, so now I'm downloading Runaway, the most mediocre adventure game series to come out of South America "mediocre" is not "bottom of the barrel" by a far shot :P Adventure games aren't a very healthy market these days
If you're lucky you get one good game a year 12:25 PM
In perturbation theory, the first order correction is orthogonal to the unperturbed state, right? Why is this the case? 1:18 PM Perturbation theory (quantum mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections... 31  Work in progress. To be updated whenever the opportunity arises. I take the liberty of compiling a list of questions on Math SE pertaining to theorems, lemmas, examples and exercises from Boyd & Vandenberghe's Convex Optimization. Please consider linking to this list whenever someone posts a new...

Goodness, that's a list Looks like that book isn't very good at explaining itself quantum computing SX has a tag for questions related to a book (currently they have 150) but then again, PSE has a million questions on Peskin and Schroeder 2:03 PM
Anybody know why you can just pull out one of those terms? Why don't you have have an extra commutator? 2:20 PM
did you try just applying it? @JakeRose [AB,C] = A[B,C] + [A,C]B Why does the gradient commute with the commutator though?
Because you need to commute it to get that from that rule @NiharKarve sorry, I forgot it's name @JakeRose Because that's how the field theoretic Poisson bracket (and hence also its quantization as the commutator) works, see en.wikipedia.org/wiki/Hamiltonian_field_theory#Poisson_bracket please the name of the operator
cyclic commutator
one 2:32 PM
That's the Jacobi property
Oh wait I guess not Ah yes, very thanks Jacobi identity...
correct
ACM changed his DP again
slereah has same one from years
I should change it too. nah these are commutators
not poisson brackets @Slereah it follows from the Jacobi property, but it's just the statement that the commutator is a derivation on the algebra of operators
@JakeRose that's why I said "how the field theoretic Poisson bracket (and hence also its quantization as the commutator)"
The commutator in canonical quantization is by definition just the Poisson bracket with some $\hbar$ stuck in there @JakeRose hint: you can pull the $\partial_i$ out of the commutator $[\partial_i\phi(x),\pi(y)]$ My DP changed
I'm Zudo, the fire kingdom king 2:40 PM
...Zudo, really? ZUKO
typo man typo 3:03 PM
@JohnRennie hey there!
sup? 3:59 PM

1 hour later… 5:11 PM
@RewCie it's "fire nation"... the title is also not "king", but whatever :P

3 hours later… 8:05 PM
Where can i find a more formal mathematical derivation of the trick where integrals involving exp(i omega t) over omega results in delta function(t=0). I've heard arguments that it is a wildly oscillating integral, so t can only be zero. 8:25 PM
@zed111 The formal underpinning of stuff like $\delta$ "functions" is the theory of distributions. Once you have established what a distribution is and what it means to take the Fourier transform of it, the derivation is as easy as saying that $\int f(t)\delta(t) \mathrm{d}t = f(0)$ is the defining property of $\delta(t)$ and showing that the integral you're describing has precisely that property as a distribution in $t$

2 hours later… 10:42 PM
Thanks @ACuriousMind

1 hour later… 11:54 PM
Hello I have a question, let's assume we have three light sensors on a table and we know their relative distances. Can we infer the azimuth and altitude angles (the distance is not needed, so only two out of three spherical coordinates) of a light point source above those sensors?
I'm trying to solve a simpler case in 2d and my intuition tells me it should be possible, but I can't find a solution