@ACuriousMind I was reading your answer regarding the density matrix. I have one initial question. The density matrix is needed when we study a sub-system, simply because we don't have full information, and that makes it looks like the sub-system,that can very well be in a pure state,is in a mixed state?

@ACuriousMind careful, that's not how it works!

you cannot get back the whole density matrix from the density matrices of the subsystems

@ACuriousMind Damn, SE making all the changes nobody asked for

> This change makes we want vomit. It's absolutely horrible. I would rather remove my teeth with a screwdriver then look at it. Please revert and throw this garbage change into the trash bin. I wish I had something nice to say, about the change, but the simple fact is I actually hate it

^ least dramatic Meta user

morning

@ACuriousMind here is one for you Disco Elysium fans

My next priviledge is that I get to protect questions

I do not wish to protect, only destroy

@imbAF No, the point is that if the full system in an entangled (but pure) state, then there is no pure state for the subsystems (that's the only correct definition of what an entangled state is!)

i.e. in that case the density matrix does not model "missing information", it models the lack of a definite pure state for a subsystem in an entangled state

@Slereah accurate :D

I should do a replay of DE

Except this time instead of being nice I just do all the drugs

@NiharKarve I have to say it does look better on my smaller screen devices, but I hate how it looks on my actual desktop, which is what I use most of the time

The Serpico playthrough

I believe in game it's referred to as the "rockstar"

I mean, you are referring to yourself as a rockstar :P

other people have...different words for that

electrochemistry is a pretty amusing voice to have in your head all the time though, so yes, the drugs playthrough is worth it!

@ACuriousMind bit weird considering I am a disco fan

Shouldn't I be the

@Slereah internal consistency is never HDB's strong suit, really :P

@ACuriousMind Perhaps I should take some LSD before playing so as to not worry about it

A disco wafer

i mean

that's not not in the spirit of the game

@ACuriousMind Is there a name for the space of matrices that are the sum of a skew symmetric matrix and a symmetric matrix of signature $(p,q)$

well, for (n,0) the name is just "matrix"

I'm not sure for the other signatures

that was the kind of matrices that Einstein used for his unified field theory

But nobody really tried to write about it since the 1930's so it's a bit hard to find a lot of rigorous details

In his book, Roland Winkler says that the substitution $\vec{p} = -i\hbar\nabla + e\vec{A}$ for an infinite-dimensional Hamiltonian. This is in a specific context. Is it possible to understand in more general terms?

@B.Brekke What do you mean by "substitution"?

assuming you're talking about the particle coupled to an EM field, it's fact that you have $\vec \pi = \vec p - e\vec A$, where $\pi$ is the canonical momentum (i.e. $\partial_{\dot{x}}L$) and $p$ the actual spatial momentum. Canonical quantization gives you that you must represent $\pi$ as $-\mathrm{i}\hbar\nabla$ (cf. Stone-von Neumann theorem), and so the spatial ("kinematic") momentum ends up as what you write there

Yes, I follow. I re-read his claim and I understand better what he means now

What is Einstein's unified theory even invariant under, a mix of the Poincaré group and U(1)???

It is good to know both, but algebras are pretty important yes

the magic of Lie theory is that the algebra contains almost all information about the group

So i should def do it ?

i.e. "focussing on the algebra" is a very normal thing for a lecture on Lie groups to do

Alright, thanks for your opnions! :3

(and btw "absolving" is a German-English false friend, it doesn't mean absolvieren in German but rather something like freisprechen or erlassen)

Damn, the potato in me got caught .

My English got ruiniert the moment i learnt german. but whatever :D

Well we don't know, maybe that lecture is so terrible it needs its sins cast out

If we have a current loop that is opened and the ends (1 and 2) are connected to a voltage source, the induced voltage is : $U_{ind}=\int_{(F)}\vec E(\vec r,t)d\vec r= \int_{(F')}\vec E(\vec r,t)d\vec r + U_{12}$ ?

Where does the induce voltage comes from?

Can someone explain this ?

First of all where does this induced voltage comes from? I am aware that a change in the magnetic flux generates that, but here we simply have a wire connected with a voltage source

Why do we get an induced voltage when we connect a wire loop with a voltage source ?

how is one supposed to find the invariants of a Cartan geometry

Or is there no systematic way and that's what the Erlangen program is