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 Jan 4 comment Harmonic oscillator identity : show $\sum_{k = 0}^{n-1} \phi_k(x)^2 = \phi_n'(x)^2 + (n - \frac{x^2}{4})\phi_n(x)^2$ Which math textbook? Dec 26 comment Operator and apparatus in quantum mechanics? Your language is really unclear... Dec 24 comment Is the Path Integral formulation of QM just a mathematical tool? I asked a similar question some time ago: physics.stackexchange.com/q/77726. The answers are good but I don't think they're completely satisfactory Dec 2 comment How to apply the Faddeev-Popov method to a simple integral I'm not sure which book does this in more detail than what you have here. But just as some basic references, there are a couple of places in the "Quantum fields and strings" volumes where this is explained: one in Fadeev's own lecture and one in D'hoker's lecture. There's also a lecture by Davide Gaiotto on BRST quantization where he explains this in his string theory course from the 2014/2015 Perimeter Scholars program. Dec 2 comment How to apply the Faddeev-Popov method to a simple integral All of this is absolutely correct and is basically how FP gauge fixing is explained in modern field theory/string theory books. Good going if you figured out this picture on your own! Nov 22 comment Inverse Lorentz transformation confusion Your question is valid, but you aren't using the right terminology. A Lorentz transformation is a matrix relating coordinates in one reference frame to another. Inverting it means taking the matrix inverse (this effectively takes $v$ to $-v$). This isn't at all the same as inverting $\gamma$. Oct 31 comment Why does Griffiths define the complex inner product differently? @B.Pasternak Relax dude, it's just notation. Pick a side and get used to the notation used in that side. If you spend more time doing physics, choose the physicists. This is just the beginning of the many notational differences between mathematicians and physicists. In the future you'll have fun with whether or not there's an $i$ in the exponent when studying lie algebras, and where to put your $2\pi's$ when doing Fourier transforms. And don't get me started on the difference in notation in differential geometry... Oct 30 comment Undergrad in QFT/GR looking to do string theory Ph.D In case you find that no string theorist is willing to supervise you or you have access to none at your institute, I would highly recommend that you try working in some other theoretical area. Modern research in CMT, or particle theory for example. The point is not to constrain yourself unnecessarily. Some research is better than none at all, which is often the case for people who only want to do string theory, since the learning curve to do research is really steep. I'd also imagine that since you say you've been generally enjoying QFT and GR, other areas of theory might also appeal to you. Oct 30 comment Undergrad in QFT/GR looking to do string theory Ph.D Are there any string theorists or people who do research in closely related areas at your current institute? If so, the best way would be to undertake either a research project or a reading course related in some way to string theory under the supervision of one of those professors. In that case if you perform well, you won't be the only one professing your interest and ability, but you'll also have letter writers doing it for you, which is immensely helpful. Oct 30 comment Undergrad in QFT/GR looking to do string theory Ph.D ... necessarily mean reading Munkres or Hatcher cover to cover is the best use of your time (it isn't). I tried this approach for a while, taking graduate-level pure math courses and what not thinking it'll be useful for string theory, and it didn't help much. Mainly because the way these concepts are applied in physics and the way physicists think about them is very different from how mathematicians present them. So in short, don't worry about math in advance. If you understand QFT and GR well enough, you can start reading string theory texts and pick up the math as you need it. Oct 30 comment Undergrad in QFT/GR looking to do string theory Ph.D It really depends on the specific type of string theory you do. I think rather than obsessing over learning specific mathematical topics which may or may not be useful, it's better to just open up Polchinski, or GSW and start reading them. When an unfamiliar mathematical concept comes up, they'll usually explain it and its physical relevance. If that doesn't satisfy you, you can then open up mathematical texts and go into more detail. Most importantly this will give you a good idea of what's useful and what isn't. Just because people say "topology" is useful in string theory (it is) doesn't... Oct 27 comment Angular momentum: why must descending and ascending chains terminate? @ACuriousMind No need to use a condescending tone. Oct 20 comment GRE practice: Total internal reflection question Completely disagree with my answer being deleted, as well as this question being put on hold. Thousands of students take the physics GRE every year and the best way to study is to work on past test problems. Thus, having this question up, as well as a full solution is completely consistent with the site being "useful to the broader community, and to future users." Sep 30 comment Definition of a line charge with Dirac delta function Yes, this is true. From this you can go on and calculate it's potential (and thus electric field) by integration. Sep 3 comment Why are WZW models interesting? I don't know much about WZW but I do know of one application: Witten's solution of Chern-Simons theory depends on it. In particular, Witten showed that if $M$ is a three manifold with boundary a Riemann surface $\Sigma$ and $G$ a group then the Hilbert space of the Chern-Simons theory on $M$ with group $G$, based on $\Sigma$ is the space of conformal blocks of the WZW model on $\Sigma$ with group $G$. This is connected to string theory since Chern-Simons shows up at all kinds of places in string theory (through "large N duality" in particular). Aug 27 comment Is configuration space in any similar to vector spaces? Ah I see! I didn't think about this carefully enough. Since the relation between position and momentum plays an important role in quantum mechanics, phase space (the total space of $M$ and $T^*M$) is what's quantized... I'll edit the answer. Aug 20 comment How does one make sense of a delta function of a scalar field? I'm not sure about the product, but one notion that might be relevant is the functional delta function. This is defined to be a "functional distribution" so that $\int \mathcal{D}\phi\mathcal{F[\phi]} \delta(\phi - \phi') = \mathcal{F}[\phi']$ i.e it picks out a specific field configuration. Aug 18 comment Boson ladder operator $n+1$ factor If you can, please do accept my answer. Aug 18 comment Boson ladder operator $n+1$ factor They're just consequences of insisting that your eigenstates be normalized, and the operator algebra of the ladder operators. Jul 3 comment Mathematician learning theoretical physics ... for all these topics is "Quantum Fields and Strings: A course for mathematicians" which was aimed at exactly what you mention: Training mathematicians to develop physical intuition and familiarizing them with modern methods (Volume 2 is more "physicsy"). It's extremely dense and quite advanced, so I would probably look at more elementary texts first.