Is it the case that whenever we observe time dependent charge distributions / current distributions, we always consider retarded scalar potential $\phi$ and vector potential $\vec A$ ?

@imbAF I don't know what you mean by "considering" there, exactly

I don't immediately think of potentials if I see a current, for one :P

Chern–Simons Theory in a Knotshell

Hi All...

Hello @JohnRennie Sir

What is the difference between method and algorithm in math not in computer science?

I have no idea ...

Why associativity is binary operation? It takes three argument and one binary operation twice.

joules law Q=W/J

1. joules law Q=W/J

2. q/t = ka(t1-t2)/l

Have you ever seen the expression $\sigma(\left <\psi \right |) = \left |\psi \right >\left <\psi \right | - 1/2 \left < \psi \middle | \psi \right >$ before?

This operator is relevant in Seiberg-Witten theory, where $\psi$ is a spinor. I was wondering if there is some classical motivation.

Moved

Hm

Apparently that thing I noticed where the synchronization structure isn't actually a proper connection has been already expanded upon in some paper

They called it a non-principal Ehresmann connection

"Although a general Ehresmann connection on a fiber bundle on which no Lie group structure is defined or considered has already been formulated (see e.g., Refs. 1 and 2). Without a group structure, the connection form is described in terms of an endomorphism field, and the curvature tensor can be reinterpreted in terms of Frölicher-Nijenhuis bracket. "'

"Note that, by the Frobenius theorem, the space distribution $S$ is integrable if $\tau \wedge d\tau = 0$ (which in coordinates becomes a rather index-trashed equation, $g_{ab} T^a \partial_i (g_{jk} T^j) + \mathrm{cycl}(b, i, k) = 0$)."

"The fiber bundle (2.7) actually is a principal fiber bundle: the group ${\exp tT }$ defines action via transport along the integral curves of T . However, this group action is not—in general—congruent with the horizontal distribution; that is, $\kappa$ is not a principal connection. The magnitude of the deviation from being principal can be measured by the Lie derivative of $\kappa$ along $T$ ; call it the torque of the observer"

I assumed so (otherwise the expression doesn't make sense)

right

in that case, one does have $\sigma(\langle \psi|)|\psi\rangle =\frac12 \langle \psi|\psi\rangle |\psi\rangle$ and $\sigma(\langle \psi|)|\psi^\perp \rangle=-\frac12 \langle \psi|\psi\rangle |\psi^\perp\rangle$ for any state $|\psi^\perp\rangle$ orthogonal to the original one

so this is basically just reflection w/r/t $|\psi\rangle$

(or would that technically be $-\sigma(\langle \psi|)$? i'm not terribly awake right now)

yeah, I typed before thinking more than one second :P

lol, i know how that goes

you're right, it's reflection if $\langle \psi\vert \psi\rangle = 2$

yeah, i wasn't worrying about the overall rescaling

one place where this reflection map did show up prominently last semester: it's the Grover step in the Grover search algorithm.

@RyanUnger is L&L field theory book (102.8) (4th edition) what you are talking about

@ACuriousMind In which case we talk about the retarded potentials?

Whenever we have time dependent sources ?>

whenever it's useful :P

I'm not sure what sort of answer other than that you're looking for here

This answer doesn't satisfy me xD

But because this was yesterday I have forgotten for what reason i asked that

Maybe later, when I revise what I read

Once in a while I just see a paper that calls the dual of a vector its metric Riesz dual

understandable but weird choice of terminology

Yes, whenever the sources have time dependence

If in a capacitor the plates are not charged

is the potential in each plate the same ?

What the hell are these Pauli matrices?

This is messed up, right?

@BalarkaSen just an unusual order and again the factor of $\mathrm{i}$