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I'm a postdoc in condensed matter theory, working mainly on cold atoms and quantum phase transitions.


1d
comment Coupling of matter field with gauge boson and Goldstone boson:
Goldstone bosons have special interactions that preserve the global symmetry to which they are related. And they can be physical in the absence of gauge field (there are a univers beyond the standard model physics). And the interaction $\phi\bar\psi\psi$ is not valid for a Goldstone mode (for the reason discussed above). It is ok for a real scalar field, but it does not produce a Goldstone (the symmetry is discrete).
1d
reviewed Edit suggested edit on QED Vertex Factor/Rule
1d
revised QED Vertex Factor/Rule
fix typos and make small corrections of the formula
Oct
20
comment Wannier Functions as Discrete Basis
1- I'm almost 100% confident that this is an approximation. 2- you're done. use that and the second equation.
Oct
12
comment Ground state of BCS mean field Hamiltonian
@Antonio_phy: You could write a more or less detailed answer to your question (and accept it), that might help someone else in the future.
Oct
12
comment Ground state of BCS mean field Hamiltonian
$|GS\rangle$ is the ground-state of $H_{MF}$, if the parameter are chosen properly, but not of $H$. Ansatz wave-functions are usually not eigenstates but only minimize $\langle\psi|H|\psi\rangle$, which is not the same thing as minimizing $E$ in $H|\psi\rangle = E|\psi\rangle$.
Oct
9
comment Clarifications needed on Gauge Fixing and Ghosts
We usually prefer that one post contains only one question, so it would be better if could create as many question as you have bullet points. And have a look at these lectures note, they might be what you're looking for : eduardo.physics.illinois.edu/phys582/582-chapter9.pdf
Oct
8
comment Expectation value of $a_i^\dagger a_i$ for thermal density matrix
You're almost there. You just need to figure out what is the value of $\sum_n n e^{-a n}$. That's easy to do by computing $\sum_n e^{-a n}$ and then take a derivative with respect to $a$.
Oct
8
comment Expectation value of $a_i^\dagger a_i$ for thermal density matrix
Use the Fock basis, and that should be straight-forward. And $\omega_n$ should be replaced by $\omega_k$ in the last equation.
Oct
7
comment Is a gapless system always conducting and a gapped system insulating?
It means that the correlation function goes to zero exponentially at long distance. In momentum/frequency, it means that as $\omega,q\to 0$, the correlation function is finite.
Oct
7
answered Is a gapless system always conducting and a gapped system insulating?
Sep
24
awarded  Autobiographer
Sep
21
awarded  Yearling
Sep
18
comment How can the reduction postulate be removed with the other postulates of QM still leading to correct predictions?
@lionelbrits: they do address your remark in the paper, see p. 143 and then section 11.3, where they explain how to recover Born's rule. It's not straightforward, but I remember that it was quite convincing.
Sep
16
comment Complex integration by shifting the contour
Agreed. I don't think it would make sense in the case of your example, but it is useful in QFT's, as it corresponds to the time-ordered propagator.
Sep
16
comment Complex integration by shifting the contour
You can also put one pole above and the other below the real axis (Feynman prescription).
Sep
13
comment Strange definition of microcanonical partition function
Yes, but that tells us more about the sociology of science than science itself. First, most people don't use either, because we usually think in terms of the (grand) canonical ensemble. Second, in most textbooks, which are only copying the previous ones, one study the microcanonical ensemble in a regime where there is no difference between the two. For some reason, $S_B$ caught up, even though Gibbs already pointed out its problems more than a century ago.
Sep
13
answered Strange definition of microcanonical partition function
Sep
11
answered How can we say that a wave function follows schrodinger equation using operators?
Sep
10
comment What is the mathematical reason for topological edge states?
That's a very nice post. Did you read all that somewhere, or did you figure it out yourself ?