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Jul
2
awarded  Curious
Jun
24
comment Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT
quantum hall droplet is a chiral CFT. From this example note that the decoupling of holomorphic and antiholomorphic part is only true for CFTs on the $\mathbb{C}$- plane. For a CFT on a plane with a boundary, or a defect, for examples, the Virasoro algebra does not decouple and you cannot solve for the holomorphic and antiholomoprhic parts separately.
Jun
24
comment Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT
say, $l_n$, and then simply copy the result for the other set. But we must always remember that the full theory is comprised of the tensor products of both sets of generators, thus, we need to tensor the holomoprhic and antiholomoprhic parts together. The physical significance of these two parts has to do with time-reversal. In a time reversal symmetric system the left and right moving parts must pair up together to cancel out, to give no net chirality. But there are chiral (time reversal broken) CFTs which have only movers in one direction. for e.g., the theory on the boundary of a fractional
Jun
24
comment Decoupling of Holomorphic and Anti-holomorphic parts in 2D CFT
Why are you talking about the Lorentz group only? Your question is about CFT, so, you want to look at the conformal group (which subsumes the Lorentz group). Now to study the conformal group we look at its Lie algebra. On the 2D plane this happens to be the Witt algebra (quantum version is the Virasoro algebra). In both cases the generators of the Lie algebra fall under two sets, $l_n$ and $\bar{l}_n$, and they obey the same commutation relations within each set, and they commute between sets: $[l_n, \bar{l}_m] = 0$. So, that means we only need to use representation theory on one set,
Jun
3
awarded  Popular Question
May
12
awarded  Nice Question
Mar
5
comment Valley meaning explanation for foreigner
@BrandonEnright No, that's not right. Valley in this case refers to Dirac points as noted below. Why valley? Because in the most commonly analyzed example of graphene, at zero doping, all the states in the bottom Dirac cone are filled, which leaves the top Dirac cone empty. This empty Dirac cone looks like a valley, like the letter 'V', and the interesting physics comes from exciting electrons into V.
Mar
2
awarded  Nice Question
Feb
16
asked Eigenvalue problem for differential equations in QM
Feb
7
comment Finding the ground state of the toric code Hamiltonian
see socrates.berkeley.edu/~jemoore/Physics_250_files/…
Feb
2
comment Confusion regarding field operators
I fail to understand the point you're trying to make about the Green's function. It is just a matter of convention. Would it help if in the field theory context I wrote $\phi = \phi_+ + \phi_-$ (see P&S)? Obviously $\phi, \pi$ will obey different commutation relations from $\phi_+, \phi_-$, but they are related to one another. Then $\phi_+, \phi_-$ in the field theory context will be equivalent to $\phi, \phi^\dagger$ in the many-body context.
Feb
2
comment What does a $SU(2)$ doublet really mean?
@SanathDevalapurkar The isospin transformation asked in this case is not a gauge transformation, i.e. it does not vary from point to point, but is rather just a global (internal) transformation. Weak isospin on the other hand is a gauge transformation
Feb
1
comment Is the spin 1/2 rotation matrix taken to be counterclockwise?
@Hunter No, what K-boy means is that you take $e^{i \theta S_z}$ (2x2) and act on it to each 2x2 component of the 3x1 column vector $\vec{S}$. You end up with a new column vector which is 3x1 with different 2x2 components. It is fine.
Jan
30
comment A point between two charges has an electric potential of zero, but a charge placed at this point will gain kinetic energy. Why?
@ByronS The two charges (or any collection of charges) will create a potential field that permeates all space. A test charge put into this system will acquire a potential energy, due to this potential field, of strength $q V$, as measured from the potential energy at infinity, $0$.
Jan
30
revised Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
added 141 characters in body
Jan
30
comment A point between two charges has an electric potential of zero, but a charge placed at this point will gain kinetic energy. Why?
@ByronS Not quite, not the charge's location. We say that we calculate the potential due to to an electric field of a point charge at point $r$ by taking another test charge which starts all the way at infinity and then bringing it to a point $r$ infinitesimally slowly. This then just measures the potential difference between infinity and $r$ which we say is the potential of the point charge at distance $r$.
Jan
30
comment A point between two charges has an electric potential of zero, but a charge placed at this point will gain kinetic energy. Why?
@ByronS To reiterate the point. When you say 'this object has $X$ PE', you really mean 'this object has $X$ PE with respect to some special point in the system'. Teachers / books which don't state this point ought to be spanked. Usually the 'special point' is taken to be the point at infinity and the potential set to 0 there.
Jan
30
answered A point between two charges has an electric potential of zero, but a charge placed at this point will gain kinetic energy. Why?
Jan
29
comment Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
(cont.) speedometer. But not all cars (read: models) have speedometers that can be found easily or at all, which is why we have to resort to estimating the speed by looking at the distance/time between the trees (read: perturbation theory). The 1D transverse Ising model is special in that it is an exactly solvable model.
Jan
29
comment Interpretation of the 1D transverve field Ising model vacuum state in a spin-language
(cont.) walls etc.) BUT! That's a separate approach from the JW transformation altogether. To draw an analogy, let's say you are in a car and you want to find out the speed at which you are moving. You have an exact solution: simply look at the speedometer. But there's an approximate way to do it: take your stop watch, measure the time between trees you pass on your way, estimate the distance of your trees, to find your approximate speed. But why do that when you can just look at your speedometer??? For the case of the transverse Ising model, the JW transformation very nicely gives you a