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1d
comment Is configuration space in any similar to vector spaces?
Not to mention that symplectic spaces are even dimensional whereas a microsecond of thought shows that configuration spaces dont have to be. Stupid me
1d
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.
1d
comment Role of special unitary groups in string theory
Forget string theory, one can't even do quantum mechanics properly without SU(2). It would be best to study how SU(2) shows up in a quantum mechanics context. SU(3) and higher show up in non-abelian gauge theory (such as the standard model) and things beyond that. Georgi's book should be a good summary.
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
20
comment Representation theory and physics
Study the representation theory of $SU(2)$. It's really important in quantum mechanics.
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.
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...
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.