The h Bar

8:12 AM

@B.Brekke I would try to give some sort of impression of Noether's theorem, because it connects the rather abstract and mathematical concept of symmetry to a concrete idea of a number being constant

Danu

8:33 AM

@RyanUnger Hi, sorry if you didn't approve of me posting it. Should I remove it, now that the reference to your old username is gone, or not? In any case, congratulations again

Danu

8:43 AM

@MikeMiller I left that as an exercise to the interested reader.

Secret

8:59 AM

iopscience.iop.org/article/10.1088/1361-6382/aba4bc

Well that is kinda interesting

It appears given 4 parties, you can have a scenario where 2 parties does things leading to party 3 to deliver a spacelike signalling in one direction to 4, even when there is no CTC involved

so there is some acausal signalling stuff going on in a CTC spacetime even when the events are not part of a CTC

Roberto Valente

Guys, my last question went unanswered, but can someone help me make sense of this comment? — “As improbable as it sounds, I suspect that when dimensionally reducing from (4+1)𝑑 to (3+1)𝑑 space, there's a magical conspiracy such that after the initial positive wavefront passes, its infinite-duration negative wake is continuously exactly canceled by successive positive wavefronts arriving from sources that are ever further-away in the fourth spatial dimension”

What does it mean by “negative wake”? “Flipped vertically” or “going on the opposite direction”? Any simple answer would suffice! …

10:47 AM

Is the Fock space of a non-interacting QFT the same space regardless of which field we have quantised?

shelton Benjamin

11:13 AM

Why is internal energy measured from centre of mass film of reference

@Charlie No, since the one-particle spaces are different for different spins and masses

(the representation of the Lorentz group is different and irreps are classified by spin and mass, cf. Wigner's classification)

11:29 AM

@ACuriousMind ahhh of course, got it, tyvm

Roughly speaking the one-particle Hilbert spaces are the functions $\mathbb{R}^n$ to $V$ for the irrep $V$, with some inner product defined so that they are square integrable

ie to $\mathbb{C}^2$ for spinors and such

Is this the "operator valued distribution" stuff?

It's the one-particle Hilbert space, so no

Here we're just considering old fashioned particles

ah

The full field Hilbert space is the Fock space built on those

11:36 AM

When you say "the functions $\Bbb R^n$ to $V$" are we talking about $L^2(\Bbb R)$ space?

Slightly more complicated, but yes

Because here, the "canonical" representation of the Hilbert space is a vector of function

So you need some kind of inner product defined, too

I'm a bit surprised to see the target space of the wave functions described as the irrep of some group

I mean why not

In the end your observable has to be similar to the classical field

so the EM field has to be a vector

Well just that when I think of the representations of a group on a quantum system I think of the Hilbert space itself as being the irreducible representation

or, not necessarily irreducible, but still

oh wait are we talking specifically about fields

No

For instance this is true of non-relativistic spinors

A spinor state in the Pauli equation is a function $(\psi(x), \chi(x))$

On which acts the infinite-dimensional spinor representation of the rotation group

11:44 AM

But the vector space in which the spinor lives is the representation of the group isn't it?

the functions $\psi(x)$ and $\chi(x)$ defined above just have the complex numbers as their target space, which isn't the representation space of su(2) in this context is it?

well the full Hilbert space vector is those two functions together

You might just be making a more subtle argument than I understand

yeah

ie $\Psi(x) = (\psi(x), \chi(x))$

This vector transforms under the appropriate infinite dimensional rep which is uuuuuh

oh ok I can see that

Something like $$\exp(i\sigma_a x^a)$$

with $\sigma$ the Pauli matrices

It's not the finite dimensional representation of this group

you're not rotating a single spinor

11:48 AM

a spinor field right

Ah, the rotation operator is $\hat U(\vec \alpha)=\exp(-i\vec \alpha\cdot\hat{\mathbf J}/\hbar)$

Secret

12:09 PM

That looks like a PR box

where the input of a pair fixes the classical outputs of two other pairs

you can check that this rotation operator leaves the Hilbert space vector invariant up to a phase

@Slereah what? The one-particle space is just the irrep

I'm talking about the infinite-dimensional unitary irreps from Wigner's classification directly on the Hilbert space, not the finite-dimensional irrep on the field target space

note that if you express the rep as wavefunctions with values in the target space, the infinite-dimensional representation is not just applying a matrix to the value, but also transforming the argument of the function

i.e. $\psi(x) \mapsto \Lambda\psi(\Lambda x + a)$, schematically

this is, once again, the confusion between the finite-dimensional rep on the target space and the unitary infinite-dimensional rep on the Hilbert space I've talked about several times now, @Charlie

12:24 PM

Sure, that's what the operator is there for

I was slightly unclear on exactly what we were talking about, I think I mostly get the difference between the two representations at this point though

@Charlie I'd advise maybe studying the Pauli equations a bit

It's the simplest case for this

No need to go full QFT to study this

Look at the non-relativistic hydrogen atom, it's the standard example for non-relativistic fermions

Yeah I had to look them up and I remember having looked them up at some point. They don't seem to come up much in standard qm teachings so I haven't really had much reason to go out of my way to learn them yet

Hence the hydrogen atom

it's where they pop up the most

yeah

12:35 PM

Landau also has a chapter for like

Non-relativistic electrons in a magnetic field

(you can also just work with free electrons, too)

on the long list of things I need to catch up on the hydrogen atom is on there somewhere :P

Bold to do QFT before the basic QM examples :p

Free particle, hydrogen atom, particle in a well, particle scattering, quantum tunnelling

oh and the harmonic oscillator

I've covered all of those except pretty much particle scattering

we did the hydrogen atom in chemistry but it's sort of a cartoon-ish model that doesn't really teach you good qm habits

so next to most topics in my long list of things to learn is a sidenote to forget everything I already know about it and start from scratch :P

I hope you remember your spherical harmonics!

You mean the big colourful pictures that show "where the electron lives"? of course!

bolbteppa

1:00 PM

I can't even remember the normalization coefficient in front of the hydrogen wave function (for the discrete spectrum!) though I've derived it maybe 10 times :(

Jim

1:20 PM

@bolbteppa be a theorist. Assume it's 1 until shown differently

Hi! everyone

Hi Dr. Nick!

@Jim to me?

I have no choice but to do that :p

Jim

@JackRod it was a simpsons reference

Jack Rod

1:23 PM

oh!

I was looking at the stat of data scientist job it is quite famous in European companies despite the fact uk has a very low number of the university which offer the courses on statistics
why is it so?

JMac

1:42 PM

@JackRod What do you mean UK has a low number of universities with courses on statistics? I'd be surprised if basically any university with math/science degrees didn't have some statistics courses.

Jack Rod

the course which especially based on a stat like bachelor in stat program

JMac

I looked up "Bachelor of statistics UK" and I see a bunch of UK schools offering a BSc in statistics.