10,692 reputation
817
bio website
location Paris, France
age
visits member for 2 years, 10 months
seen 18 hours ago

18h
comment Undefined result of relativistic velocity addition formula
To see a acceptable limit, begin by choose one of the velocities (say $v$) to be $c$, then $u=c$ for all $v' < c$. Now, you may take the limit $v'=c$
18h
comment Is the ground state of a QFT always a pure state? And excited states are mixed?
It is not directly relevant to your question, but there should be a holographic point of view too. Following the classical paper Holographic Derivation of Entanglement Entropy from AdS/CFT, of Ryu, Takayanagi, a thermal state in the $CFT$ (entanglement entropy at finite temperature) is compatible with an area law in the AdS (formula $2.9$).
19h
comment Infinitely many degeneracy of Landau level: Countable or Uncountable?
There is an infinite degeneracy in the symmetric gauge too. See this interesting paper, for instance formula $3.5$
19h
comment Left (right) invariant vector fields on superspace
The $D_a$ anticommute with the $Q_a$, and so transform a superfield into an other superfield. $\delta_ξD_aφ(z) = D_aδ_ξφ(z) = iD_a(ξQ + \barξ \bar Q)φ(z) = i(ξQ + \barξ \bar Q) D_aφ(z)$ . So they are supercovariant derivatives.
1d
comment Quantum ring and Dirac Quanitzation
@BRayhaun : So, $g(\vec r)$ is constant inside a homotopy class. The example I gave in the answer correspond to the $1$ st class or $1$ winding number.
1d
comment Quantum ring and Dirac Quanitzation
@BRayhaun : You have different homotopy classes for the closed paths, each one corresponding to some winding number. These are called homotopy classes, because, inside one class, one may go continuously from one closed path to another (without crossing the solenoid). In fact, here, the 1st homotopy group, the fundamental group is just $\mathbb Z$. Closed paths which are not enclosing the solenoid correspond to the $0$ th class or $0$ winding number.
2d
answered Quantum ring and Dirac Quanitzation
Sep
17
comment How can I write a Gaussian state as a squeezed, displaced thermal state
@FraSchelle : Now, in my last ref, a "gaussian" state is diagonal in the coherent basis ($3.86$), and is also diagonal in the Fock basis ($3.87$), but it does not appear "gaussian" in the Fock basis.
Sep
17
comment How can I write a Gaussian state as a squeezed, displaced thermal state
@FraSchelle : If you inverse the order of $S$ and $D$ (relatively to the OP), the result in my first ref is correct (I have checked the mean, but the variance should be correct too), and it gives a formula between mean, variance, $\zeta$ , $\alpha$, and $\bar n$ (which was the OP question).
Sep
16
comment Why are non-Abelian gauge theories Lorentz invariant quantum mechanically?
I found a curious paper, where the "gap" is resolved, by using some "deformed Lorentz transformations" applying only on the non-physical (scalar, longitudinal) degrees of freedom. Abelian and non-abelian cases are studied (see for instance formulae $(3.2), (3.7)$.
Sep
16
revised Typical form of the beta function of the renormalization group
Completely rewritten...
Sep
16
answered Typical form of the beta function of the renormalization group
Sep
16
comment Why Are Normal Shock Waves Unstable in a Converging Channel?
In the Kantrowitz paper, you might see directly formula $(31)$ page $25$, with $3$ different cases (formulae $(32)(33)(34$) page $26$, and the discussion at the bottom of page $26$), going with Fig .$8$ at the end of the document. I am not a specialist, so I suggest you to ask a new question by describing precisely what is not clear or what you don't understand in this paper.
Sep
15
comment Highest weight unitary representations of $psl(2|2)$
For $1.a$ and $1.b$, there is a discussion pages $23, 24$ (document numerotation) (and more generally chapter $2.2.1$) in this paper
Sep
15
comment String frame and Einstein frame for a Dp-brane
At the end of the page $53$, you see that the action in the Einstein frame, and the dilaton field is the same that in equation $(39)$. The metrics, in the Eistein frame, in $10$ dimensions is simply $ds_E^2 = e^{\phi/2} ds^2$
Sep
13
comment Doppler effect and acceleration's impact
In your text, the reception of the sound is supposed instantaneous. However, if you want to study the pheonomena along some amount of time, you might be interested by a previous answer to a similar question.
Sep
11
comment How can I write a Gaussian state as a squeezed, displaced thermal state
Probably you could demonstrate the result thanks to the action of $D$ and $S$ on $a, a^+$ (see pages $15$ and $28$ of this presentation), and the expression of the thermal density matrix in the Fock basis (see $(3.87)$ in this ref)
Sep
11
comment How can I write a Gaussian state as a squeezed, displaced thermal state
There is a result (without demonstration) in formula $(11)$ (and following lines) of this paper. A pseudo-commutation relation for $D$ and $S$ is given in formula $(15)$ of this paper
Sep
11
comment Hawking Radiation and virtual particles
@JerrySchirmer : There is a change of signature in the Schwarzschild coordinates (time, radius) at the horizon, so the "energy" of the ingoing particle, seen by an observer at infinity, seems to be more a (negative) radial momentum. Is is not possible to consider a process with $3$ actors (black hole, ingoing particle, outgoing particle), where, by conservation of energy, the energy has to be lost by the black hole itself?
Sep
11
comment Why Are Normal Shock Waves Unstable in a Converging Channel?
Yes, good job .