I spent ~30 minutes staring at a problem in my GR book wondering how he managed the answer when I finally decided to check the errata to see the answer was wrong :(
The problem was rather trivial (using $T^{\mu\nu}=f^\mu h^\nu$, find the transformation $\bar{T}^{\mu\nu}$ by transforming $f^\mu$ and $h^\nu$--his original answer said $\bar{T}^{\mu\nu}=-T^{\mu\nu}$ so I sat wondering how $\partial\bar{x}^\mu/\partial x^\gamma\,\partial \bar{x}^\nu/\partial x^\delta=-1$).
Thus, physics authors who treat (mathematically) advanced topics use Latin indices in accordance with the mathematical literature they are referring the reader to.
As with all notation, there are examples for and against this.
You end up having to project various quantities into the plane spanning the $1-2$ direction. $m$ is just another index for those directions.
2 hours later…
user54412
2:40 AM
@Danu I can't find it, or even so much as an abstract for it, with any resources at my disposal. I did however come across this independent discovery from a couple years later.
user54412
I actually wonder how many of the citations to Nordström's paper read it, given how obscure it it.
@0celo7 In the theorem-proof format, you can read the theorem, understand the proof, then repeat on the next topic. If you don't understand the theorem then at least you know exactly what you don't understand. In lecture format it's hard to follow once you get stuck, and it becomes ambiguous as to what it is that you don't understand.
I have homework from Georgi on the restrictions of dynkin diagrams (& classification of the compact semisimple groups) so this is a perfect topic to look into.
The general idea is this: Let $\Gamma=\partial \Omega$ be a curve in $\mathbb{C}$. Then by Stokes': $$\oint_\Gamma f\,\mathrm{d}z=\int_\Omega \bar\partial f\,\mathrm{d}\bar z\wedge \mathrm{d}z=0$$ if $f$ is analytic.
@NeuroFuzzy This type of thing is to be formally understood in the context of complex differential geometry. I don't think that book addresses that rigorously.
@0celo7 yeah I remember that in my complex analysis class we weren't able to use anything related to $\frac{\partial}{\partial \bar z}$ because it's a bit wonky to define. It's probably doable in a totally rigorous way using multivariable stuff.
How would I evaluate the surface charge density on the inner and outer surface of a neutral, spherical, conducting shell which has an off-centre charge $q$ inside? I believe that we can not use the method of image charges since even though we know the potential of the shell is constant we do not ...
I actually read that the RN solution is not at all like the field of an electron because it lacks things like spin & magnetic dipole moment
@Icosahedron I don't think this is the right approach.
@NeuroFuzzy That's just classifying the symmetry groups of crystals as far as I know
@DavidZ I wonder: What about answers like this. I personally think they're useless and should be flagged, but I'm not sure if that's actually right according to site policy.
@Waffle'sCrazyPeanut hm, well, I tend to be a little more lenient about asking for methods, rather than asking for answers. After all, if someone comes to us and says "I have to solve this problem, I tried X, Y, and Z, but none of them work because [...], [...], [...]; is there another way?" I think that should generally be fine
@DavidZ But, that doesn't agree with our policy, right? I thought we encourage only those homework questions which demand the concepts underlying a particular problem, not the ones which ask for methods or formulas to solve the problem (the latter is pretty much useless anyway))
Well, "what methods can be used to solve this kind of problem?" is a conceptual question IMO
This is a case where we have to use some judgement to distinguish the people who are trying to get us to do their homework for them from the people who are legitimately stuck on a real, difficult problem
@Danu well, it never hurts to flag anyway
I think that answer probably doesn't quite qualify as an answer in its current form, but it's close
The basics are just quantum field theory, for which I'd recommend Griffiths' particle physics, and then either Peskin & Schroeder or Srednicki, or something equivalent
Yeah, I wasn't recommending those as QCD books specifically, but rather as QFT books. You have to become comfortable with quantum field theory as a framework before getting into the specifics of QCD.
Yeah... there's a nice book by Yuri Kovchegov and Eugene Levin, "Quantum chromodynamics at high energy", but it starts well above the level of P&S. They cover all the stuff I think you want to learn in the first two pages, and go forward from there.
I think it's more that not many people are interested in writing high-level overviews at that level. There are plenty of books, but they all go into detail about the math. The goal is always to train people to do calculations, not just to give a conceptual understanding.
That's the thing. I'm not interested in QCD for the sake of applying it professionally. I am very interested in the general ideas involved in constructing gauge theories though, and QCD is obviously a very good place to learn about them.
Well, the only way I know of to learn about the general ideas involved in constructing gauge theories is on the road to learning how to apply them.
You might find something more up your alley if you look into the mathematical physics community. I'm not involved in that sort of work at all, so I couldn't give you any specific recommendations though.
If you can find a good review paper on the foundations of nonabelian gauge theories, and look at the list of references it cites, that might be a good place to start. But I don't know of any such paper. (I'm sure they're out there, but I haven't read them.)
Well, there's a lot of manual calculation that goes into it before you can get a computer involved
like in the case of my research for example: my boss and a couple of his collaborators wrote a very long paper (like, a year-long project) on the theoretical calculation of the pA->hX cross section alone, all before we started doing the numerical implementation
In general, it's mostly fussing with code. The bulk of this latest project was about transforming the expressions for the cross section into a form that would allow the computer to evaluate them without too much uncertainty.
We went through a bunch of different expressions before finding the right forms that worked. So I'd spend my time either doing the math to convert the formulas into the latest form, or taking that form and typing it into the computer.
Alright :) In your work, do you end up finding a lot of stuff (obviously it will be quite specific and perhaps small, but that doesn't matter) that still make you go like "huh, nice!" and feel good about doing physics?
Mostly it's frustrating - I'll get some new formulas, put them in the program, wait like two days for the code to run, and then the results look terrible
@Danu I'm not really sure that I am satisfied with my work. Satisfaction for me would come from knowing that I contributed something valuable - something to justify why it needs to be me doing this work, not just some random person (with a PhD in the right subject) - but I haven't really had that moment.
That being said, there were a couple times where we got really good looking results, which was nice
I think different people are looking for different things in research. Maybe you will appreciate the abstract stuff more.
Personally I don't want to be too disconnected from reality. To me the reason science is so interesting is all about matching predictions to experimental results.
I had similar ideas once upon a time, but in the other direction: I wanted to learn the mathematical foundations and the practical applications, even though I was definitely more interested in the latter. Then I decided it was too much work. It's nice to not have to care about the foundations when I don't want to.
next semester I'll be doing effective field theory, ST 1, gauge-gravity duality and CFT as physics courses, and topology and symplectic geometry as math courses
Hahaha, and you're there to make me famous for some obscure prediction by validating it, right? ;)
The main drawback of doing some mathy stuff is that it feels so bad to do physics-math (hence the stuff about groups in QCD). Nobody even cares about getting the terminology right!! Super confusing for someone trying to learn the mathematics and physics at the same time
@DavidZ ...so now I'll return to my discussion of extremal Reissner-Nordström black holes, which have fine-tuned charges so that they exactly mimic the Newtonian situation of balancing gravitational and electrostatic forces between point particles ;)
The Einstein field equations reduce to the Laplace equation!!! :D
I couldn't promise to read them - I only have so much free time - but if you feel like putting them up online somewhere just in case, that'd be cool. If I do wind up having time I would be interested to see them.
So if the ODE for h depends on h(R) and h'(R), what you want to do is to guess the values of the latter and then solve the ODE to see if those values were right. If not, adjust the guesses. i.e. you do pretty much exactly the same thing as I did to find R and h(0)
I posted an review comparing my experiences in physics stack exchange and at physics overflow.
It was clearly an answer the the question "how are they different from each other?"
This was purely from my point of view.
There were suggestions for improvement to Physics stack exchange. Which if...
@ACuriousMind I see what you're saying, but that doesn't make me non-hedonistic because surely people can accept that I derive pleasure from it, so I'm pursuing pleasure.
@ACuriousMind Unrelated math question: Suppose we have two curves $\gamma(t)=\exp tv$ and $\lambda(t)=\exp tw$. Is $\exp t(v+w)$ expressible in terms of $\gamma$ and $\lambda$?
$v,w$ are vectors at the start point of the curve.
@Prathyush Hah, nice try turning stuff around. I see that you are not interested in a serious discussion and have come to rant once more ;) Have fun with it, and enjoy the attention while it lasts! — Danu39 mins ago
@ACuriousMind My personal experiences here defines what constitutes as differences between physics overflow and Physics stack exchange. I have already made it clear to HDE226868, If you open my question physics.stackexchange.com/questions/44647/… I would reconsider not pursuing this anyfurther. Other wise I will modify my answer to indicate that there as been atleast one instance of ABUSE and I would be fair in making that call. — Prathyush2 mins ago
I posted an review comparing my experiences in physics stack exchange and at physics overflow.
It was clearly an answer the the question "how are they different from each other?"
This was purely from my point of view.
There were suggestions for improvement to Physics stack exchange. Which if...
