12:09 AM
@Semiclassical the wiki refers to $N$ as a 'generalized' particle number, i.e. the qft $\hat{Q}$, in such (relativistic) cases

8 hours later…
7:48 AM
morning

8:38 AM
afternoon

9:06 AM
nlab is down
nooo

9:16 AM
I am inputting some actual diagrams into VQGAN to see how the evolve

great, Cthulhu has learned how to do math diagrams
3

hey, we may learn some dark secrets from this
I'm gonna do something even worse and try it with the physics page from the Codex Seraphinianus
Actually getting less scary

10:18 AM
Fun results you can get from the Codex

2 hours later…
12:38 PM
@bolbteppa ah, nice. So maybe the problem is simply identifying in what sense you have equilibrium
with the real problem being how tf you deal with non-equilibrium systems

12:56 PM
Accidentally put a PDF of the Donald Duck family tree in my science folder
woops

1:36 PM
@Slereah genealogy is a science, too :P

I guess I can put it in the Humanities folder
it's about as good as most papers there

2:22 PM
Is electrical air breakdown what happens in lightning strikes or lightning and electrical breakdown different phenomenon?

2:36 PM
I’d say it’s the same physics, yes
Though lightning is certainly a complicated macroscopic phenomenon. You don’t see one arc but many
(And then there’s the weirdness that is upper-atmospheric lightning)

3:00 PM
@Semiclassical can you explain what happens in lightning

According to greek philosophers it is due to cloud collision

@cOnnectOrTR12 ...have you tried reading e.g. the Wikipedia article?

Is it breakdown of air causing e to move in the opposite direction of the field , where collision with atoms emit light. And we can see it as lightning
@ACuriousMind idk what are leaders and upward streamers and well

"In a process not well understood, a bidirectional channel of ionized air, called a "leader", is initiated between oppositely-charged regions in a thundercloud."
what's unclear about that, except that it's very clear that we don't entirely know what's going on?

3:19 PM
@ACuriousMind can I take the explanation of air breakdown as lightning

I don't understand the question.

What I wrote about what is electrical breakdown, can I call it lightning

electrical breakdown is not lightning
what happens before lightning is that the air gets ionized, like the Wiki article says. "Ionization" is just another word for "electrical breakdown"
but there's a substantial difference between just having ionized air and having actual lightning - you can have ionized air without having the gigantic energies of a lightning strike travelling through it

@ACuriousMind when the field between two regions is strong enough it would rip out electrons from atoms. These collide with other atoms creating light. What is this light then if not lightning

@cOnnectOrTR12 lightning is the current flowing through the channel of ionized air, not the mere existence of the plasma
also, the light from lightning is blackbody radiation because the air plasma gets so heated by the current flowing through it, it's not about specific collisions caused by the ionization
you don't get lightning juut from having a strong field, you get it from having a strong field and then moving a lot of charge quickly through the ion channel that strong field creates

3:37 PM
@ACuriousMind so strong field will create plasma not lightning. But where do these lot of charges come from if not the electrons freed up recently by the strong field

@cOnnectOrTR12 1. If you'd read the Wiki article you'd know that (or at least what speculations exist). 2. Where do you think the strong field comes from if not from a lot of charge sitting somewhere waiting to be discharged?

So the plasma is created by the collision of ions with freed electrons. And through this channel or path the lot of charges flow creating more current and light. That is lightning

3:55 PM
@ACuriousMind Right?

4:22 PM
@ACuriousMind I read the article and what I understood from that is that due to the accumulation of charge in one region strong field is created. This strong field start ionising the air molecules causing it to lose electrons. A path of ionised air or channel builds up in zigzag fashion which move downwards. Same way a path of leader moves upward from the ground. When these two paths meet they create strong electrical discharge known as lightning

4:50 PM
I think we've found our next HNQ

5:21 PM
@NiharKarve if you mean the "flappy" question, I think there's filters on what sort of words can appear in HNQ titles that'll prevent it from going hot

boo
the world has a right to know

5:39 PM
@ACuriousMind can you verify?

6:00 PM
@cOnnectOrTR12 well, as the article says, we don't really understand how the ion channel is formed. I'm not sure why you insist on me approving or not approving of some simplified summary - if you're fine with that explanation, what does it matter whether I think it's good?

@ACuriousMind maybe because you are better in physics

sure, but I'm also a pedant :P

Mee too . I like to know things correctly. That should be right information. Not that I have misunderstood

6:28 PM
Does anyone have a pdf copy of the book Applications of Spinor Invariants in Atomic Physics?

6:44 PM
pedantic physicists
hmmm

all pedantry is relative :P

How pedant are you

77%

How did you calculated
Joke

2 hours later…
8:33 PM
Why do people go on about Clifford Algebras so much?

because spin

What additional information does studying Clifford algebras provide compared with studying the representations of the Lorentz group?

the Clifford algebra is the algebra generated by the $\gamma$-matrices
its unique irrep is the Dirac spinor representation, and Dirac spinors are pretty central to quantum theory

it also easily generalizes to any dimension

Ah okay
Why don't we explicitly write all fields in terms of Dirac spinors?
fields that transform under the $(0,0)$ rep of the Lorentz group should be able to be written in terms of Dirac spinors right?

8:43 PM
why do you think that?
the Dirac spinor is $(1/2,0)\oplus(0,1/2)$

Oh sorry my mistake
Shouldnt I be able to construct a scalar from Dirac spinors?

well, there are some scalars you can construct from it, sure

There is a certain subset of solutions to the Dirac equation that are also solutions to the KG equation right?

I mean, a scalar field is a dirac field of zero components, I guess?

the kinetic term in the Dirac Lagrangian is a scalar, for instance

8:47 PM
the Dirac bilinears, as they are called

why does the universe have a spin structure

Shouldnt the whole Lagrangian be a lorentz scalar?
Isn't that an axiom or something

@DIRAC1930 sure

The Lagrangian is an $n$-form, technically
Although usually just by adding a measure form at the end

@Slereah that's just a technicality whether you think the $\mathrm{d}^nx$ belong to the Lagrangian or to the action

8:49 PM
The $L$ itself is mostly just a boring scalar

@RyanUnger why is the universe a manifold?

Do Dirac spinors just arise because of the fact that inner products in QM are independent of phase?

Guys

@DIRAC1930 not really (because the Dirac equation is an equation in 4 components while the KG equation is an equation in a single component), but each of the components of a solution to the Dirac equation also fulfills the KG equation

Someone know if the Cauchy Riemann integral can be used when the residue is at the contour of the curve?

8:52 PM
@DIRAC1930 I don't know what you mean by that
Dirac spinors "arise" because they are a possible projective rep. of the Lorentz group, and it turns out they're pretty common in nature

I thought the projective reps. arrise because we only need to consider the representations up to a phase due to the inner product being invariant under phase transformations or something

@ACuriousMind I don't understand how that's a response

@RyanUnger I just think that we just have to add "the universe has a spin structure" to our axioms when we do GR physics with spinors, just like we have "the universe is a pseudo-Riemannian manifold" when we do GR

Being invariant under phase transformation implies conservation of charge, not?

Don't confuse things
Phase of the wavefunction isn't phase of the field

8:56 PM
@LSS no, it doesn't, see this answer of mine

I wish there was a little booklet summarizing everything important

we call these booklets "textbooks" :P

Lol

and the reason there are so many of them is that everyone disagrees over what, exactly, is important

Thats true
I think understanding the Lorentz group fully is very important

9:03 PM
@Slereah What language is that
w

@LSS None.

lol
Anyway, beatiful diagrams.

It is very aesthetic
check out these nonsense diagrams

9:18 PM
Are the representations of the Lorentz group the same in classical physics except for not having $n,m = N/2$ for $N$ being an integer?
@Slereah Bottom three rows are string theory
3rd row are feynman diagrams

@DIRAC1930 you can have spinor fields in classical physics
I don't think there are any in physical situations
But nothing is stopping you

Okay
When did people know which rep the EM fields transfomed under?

As soon as they applied representation theory to physics, I assume
it's not a super hard case

Maybe I should start there
in that case