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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.
Jul
3
comment Mathematician learning theoretical physics
...a book written by a physicist when it comes to rigor. For the more quantum topics, chapters 8-10 of "Mirrror Symmetry" by Vafa, Hori, Zaslow et al (a book aimed at both mathematicians and physicists) should provide a very quick introduction to quantum mechanics, supersymmetry and path integrals, though it would probably need to be supplemented. For more detailed treatment of QM I recommend Shankar. QFT is always a tricky subject and no one book is good enough. I like Tom Banks' book and also Pierre Ramond's book, and Mirror Symmetry also provides a good picture. Finally a very advanced...
Jul
3
comment Mathematician learning theoretical physics
...need to internalize is symmetry and variational principles, as they are at the heart of physics. Landau/Lifschitz (not all the chapters are necessary though) is a good start followed by a more geometric treatment (like Arnold's). You can continue your study of mechanics with other "classical" topics such as electromagnetism, gauge theory and general relativity. I found "Gauge Fields, Gravity and Knots" by Baez to take a good middle ground between math and physics (it also provides good references). For a more thorough treatment of General Relativity, Wald's book is as good as it gets for...
Jul
3
comment Mathematician learning theoretical physics
Indeed working through a typical freshman/sophomore level physics book would be a waste of time: No one who works on abstract theoretical physics topics such as supersymmetry and string theory ever uses the "Lensmaker equation" or stuff about heat engines in their research (however topics like classical mechanics and electromagnetism do help in developing physical intuition to an extent, so study those if you can) So indeed your guess is correct in that you can jump straight into the more abstract treatments. Now let me make some recommendations. For classical mechanics, the basic thing you...
Jul
2
comment Calculating euler number of disk
As for the equivalence of the two formulas describing the geodesic curvature, I'd have to think about it since I've only explicitly worked with the classical one I wrote above. It is written out in terms of Christoffel symbols here: mathworld.wolfram.com/GeodesicCurvature.html
Jun
30
comment Doubts taking the second functional derivative of the Klein Gordon action
The main property you need to apply is $\frac{\delta \phi(x) }{ \delta \phi(y)} = \delta(x-y) $.
Jun
22
comment Hamiltonian related to Riemann zeta function
I believe he's asking whether the Hamiltonian above is meaningful/makes sense.
Jun
20
comment How do you take the derivative with respect to a rank two tensor?
The answer is correct, but you need to fix the index positions in your example.
May
28
comment Question about scalar product of 2 four-vectors
Ah yes, that's the standard way of writing it. Glad it helped!
May
26
comment Elliptic genus; What is it within string/M-theory?
Chapter 10 discusses the relationship between the Euler characteristic and the Witten index (pages 206-211) and also the general properties of supersymmetric theories. The elliptic genus is a generalization of these results, so it's good (almost necessary) to have these concepts down first.
May
22
comment Fermionic path integral on the disk - Recovering the vacuum state
Thanks for your patience, Lubos.
May
22
comment Fermionic path integral on the disk - Recovering the vacuum state
I'm afraid I might be misunderstanding some of what you're saying. Why would integrating over the boundary configurations confirm our answer? And since the ground state, like you said, is independent of half of the Fourier modes wouldn't integration give zero? Are you suggesting that since an explicit path integral can't give the answer the answer in above form therefore, I should verify it by other means (integration?). To reiterate my confusion, what I'm looking for is a sketch as to how one would recover the expression of the ground state using the path integral. Is that possible to do so?
May
22
comment Fermionic path integral on the disk - Recovering the vacuum state
Dear @LuboŇ°Motl. Please see the edits.
May
22
comment Fermionic path integral on the disk - Recovering the vacuum state
Dear Lubos, I'm not sure I follow. I have the wave function expression for the ground state which I got independently from the operator formalism, and which depends on infinitely many Grassmann variables. I'm now just trying to see whether the path integral gives me the same result. The classical action giving zero (I think) implies that the ground state doesn't depend on the boundary conditions, which isn't true once we look at the wave functional expression.
May
21
comment Fermionic path integral on the disk - Recovering the vacuum state
Thanks Lubos. Yes the issues you point out all need to be addressed (they mainly come from using the action on the cylinder rather than the disk), however they are not what's troubling me. I can't see what to plug in for the $\psi$'s and integrate over. The classical solution with boundary conditions would be simply that the $\psi's$ are either left of right moving. But plugging this into the action gives me zero.
May
14
comment Why two different Lagrangians to derive geodesic equations?
Sorry for the late response, but I just mean that it follows from applying $\frac{dx^{\mu}}{d\lambda} = \frac{dx^{\mu}}{d\tau}\frac{d\tau}{d\lambda}$. If further clarification is required, please ask it as a separate question and I'll be happy to go into more detail there.
May
13
comment Why two different Lagrangians to derive geodesic equations?
One simply applies the chain rule for that, if I understand your confusion correctly.
May
13
comment Why two different Lagrangians to derive geodesic equations?
I'm not familiar with the source you're using, but the clearest (IMO) way to get the affine geodesic equations from the square root Lagrangian, is to first get the non-affine equations, and then switch your arbitrary parameter to an affine one. As far as having a source for the derivation, I don't know of any which derives the non-affine equation directly (although it's not difficult). Carroll in his notes starts with the square-root Lagrangian and then changes to an affine parameter in the middle of his derivation. Look at page 15 in: preposterousuniverse.com/grnotes/grnotes-three.pdf
May
11
comment $su(1,1) \cong su(2)$?
@LuboŇ° Thanks for the clarification. It was the first time I had seen the $SU(n,m)$ notation being used.
May
11
comment $su(1,1) \cong su(2)$?
What exactly do you mean by $su(1,1)$? Is it the same as $so(1,1)$ by any chance?