The h Bar

Danu

21:00

@DanielSank Is it a "definition-theorem-proof style" book?

0celo7

@DanielSank Please sent it to me.

You have my email.

Danu

@ACuriousMind Because some of us still have some catching up to do in terms of GIFs viewed/time alive ;)

John Duffield

@ACuriousMind : chat looks like a broken instrument board because you won't talk physics. How about talking about time dilation? See if you can point out any problems with this here little answer of mine.

DanielSank

1) Vectors can be expressed in various bases. This is obvious if you draw an arrow on a piece of paper and draw two different coordinate axes.
2) It's useful to talk about linear transformations of vectors.
3) Those linear transformations can be expressed as matrices, but doing this requires a basis choice.
4) Changing a matrix/vector from one representation to another involves a transformation (which is unitary), and that transformation has the same matrix in the two bases it connects.
5) Integration and derivatives are linear operations. The exponentials diagonalize derivatives.

@Danu No.

Danu

@DanielSank So what kind of things do you write about?

DanielSank

21:02

@Danu It's a "This is pretty simple so let's make it as obvious as possible, with examples and really useful exercises" style book.

Danu

@DanielSank Ah

DanielSank

@Danu Yes, this sounds obvious but I'm not aware of any other document which takes this approach.

@0celo7 Ok will do in a second on one condition: you agree to actively send feedback about unclear sections, organizational issues, etc.

Ok?

Danu

But you're not doing the usual things like you know proving convergence and shit

DanielSank

@Danu Absolutely not.

Danu

@DanielSank Hey I'll also gladly do this

DanielSank

21:03

That's a complete waste of time IMO.

0celo7

@DanielSank Sure. I don't promise to read the whole thing, of course.

DanielSank

@0celo7 Ok then it's a deal.

Danu

@DanielSank Ahem... For physicists

ACuriousMind

@DanielSank How do you explain that the Fourier transform relates the function on a (continuous!) interval with functions on a (discrete!) lattice in that "change of basis" point of view?

Danu

We don't have a patent on Fourier analysis :P

0celo7

21:04

@Danu *GDP production

DanielSank

@ACuriousMind You just point out that $f(x) = \langle x | f \rangle$ for some abstract vector $f$ and then move on with your life.

@Danu Meh.

ACuriousMind

@DanielSank I don't follow

Danu

@DanielSank Honestly though, I think it's cool 'n' all for us to ignore those issues, but you shouldn't try to deny that those things are useful in other respects.

0celo7

@ACuriousMind Is Stone-von Neumann the one which says $p=-\mathrm{i}\nabla$ is the unique rep?

Danu

(Google is your friend)

0celo7

21:06

huh?

ACuriousMind

@0celo7 You know, you could have just googled "Stone-von Neumann theorem"

Slereah

Guys

0celo7

@ACuriousMind huh

Slereah

Is there a general theorem when a green function is just the solution * $\theta(x)$

Because that kind of solution pops up often

DanielSank

@Danu Dude, even if you're a math student, you will pass through a point in your life where you need to understand wtf is going on without all the epsilons and deltas.

@ACuriousMind What don't you follow?

0celo7

21:08

@ACuriousMind What do you actually mean by this?

ACuriousMind

@DanielSank But they are still interested in convergence, they just leave behind the need to prove it in the excruciating detail of hte epsilons and deltas

Danu

@DanielSank Yes. But as a mathematician you also need those things---I'm not objecting to you skipping it, just to your assertion that it is a "complete waste" of time.

ACuriousMind

@DanielSank How your reply answers my question. Like, at all.

DanielSank

@Danu Fine, it's a waste of time for anyone at the stage that they should be reading this text.

@ACuriousMind Then I failed to understand the question.

ACuriousMind

@DanielSank Periodic functions have discrete Fourier transforms.

Danu

21:09

@DanielSank Okay :) So can I see a copy? :D

DanielSank

@ACuriousMind Oh ffs ok yes that requires extra discussion.

Slereah

@ACuriousMind Deltas everywhere

Danu

lol

Delta's are god damn functions :D

0celo7

I don't think I've ever seen a Fourier transform in GR

DanielSank

Whatever... if you just think about it for half an hour you can figure it out. But you're right, I should put something about the Poisson summation formula in there...

ACuriousMind

21:11

@DanielSank Okay

0celo7

Maybe g wave shit

Danu

Poisson resummation?

Slereah

@0celo7 Source term in linear GR

Danu

Oh, not resummation

0celo7

@Slereah what about it

Danu

21:11

Annoying that there are 2 different things with such similar names.

Slereah

It's all Fourier shit

DanielSank

@Danu This

6

Q: What is the sum over a shifted sinc function?

What is the sum of a shifted sinc function: $$g(y) \equiv \sum_{n=-\infty}^\infty \frac{\sin(\pi(n - y))}{\pi(n-y)} \, ?$$

Slereah

There isn't a lot of Fourier in GR because GR is non-lineae

DanielSank

See the part about Poisson summation.

0celo7

well I don't care about linear GR

Slereah

21:12

But linearized GR, you can use Fourier 'til the cows come home

Danu

@DanielSank It's fine---I just learned about Poisson resummation in CFT and that's something different so I was confused.

ACuriousMind

@Slereah Yes, I know you can think of them as a nice Dirac delta comb, but that would require introducing distributions

Slereah

@ACuriousMind Everyone loves distributions!

Danu

Delta's are god damn functions

:D

0celo7

@Danu mb I should talk about that

it's in BLT, right?

Slereah

21:13

$\delta(0) = \infty$

Danu

@0celo7 Blumenhagen

Slereah

Good way to bother a mathematician

ACuriousMind

@Slereah ::eye twitches::

Keep these mind

I know that for some people (1 or more) Fourier is everything, like a stance.

Slereah

Oh wait

DanielSank

21:14

@ACuriousMind Take that.

Slereah

I can do worse

$\delta(0) = \aleph_0$

ACuriousMind

@Slereah Have mercy!

Slereah

$\delta(0) = \aleph_0 + \omega + \infty + \text{Card}(\{ x \vert x = x\})$

0celo7

@Slereah so, is $2^{\delta(0)}=\aleph_1$?

Slereah

Yes, that's the Dirac distribution for the space of all functions

0celo7

21:15

Don't they do that in Faddeev-Popov

@DanielSank 2006?

34 pages?

I was expecting 800+

@DanielSank do you need someone to solve the exercises

@ACuriousMind Shitty notation ;)

I guess Mr. Daniel Sank disagrees

DanielSank

Whatever, I'm considering dropping that entire section.

0celo7

Mar 3 at 20:10, by Chris White

@0celo7 marking every vector indiscriminately with a ket is akin to marking every vector indiscriminately with an abstract index -- it is indicative of the author fundamentally not understanding the structure of the mathematical objects they're working with

@ChrisWhite you should fight DS

Danu

@DanielSank The vector space axioms? :P

DanielSank

@0celo7 Wow.

Danu

@DanielSank Uh-oh :P

DanielSank

21:19

@Danu I wrote most of this when I was an undergraduate. This whole thing happened because my quantum mechanics professor started talking about momentum space and using Fourier transforms and nobody had any idea what he was on about.

0celo7

@DanielSank why is $V$ bolded?

DanielSank

Then he said "look, it's just a basis transformation" and everything clicked.

0celo7

Shankar's QM books states this multiple times

DanielSank

I wrote this document because I realized that nobody in my class (or department) really understood how these things were related.

0celo7

mb that's why I don't get why you're writing this

DanielSank

21:20

@0celo7 Yeah, well that's why I recommend Shankar, but we didn't use it in undergrad.

0celo7

@DanielSank your example with the two masses is straight from Shankar

DanielSank

Go look around on main. You'll see people recommend Griffiths to n00bs.

0celo7

> The symbol $|\,\,\rangle$, called a ket, indicates a vector.

Danu

@DanielSank Hey, I like Griffiths.

I also never really used the Fourier transform in that book.

DanielSank

@0celo7 Yeah, I found later that Shankar does some, but not all of what's in my document.

Danu

21:21

As far as I remember...

0celo7

@DanielSank the typesetting could be refined, I'd be happy to do it while reading...

DanielSank

@0celo7 Please don't pepper chat with specific comments about it.

It's in a github repository. Just file issues and pull requests.

0celo7

> Keep in mind that |v + w> is
simply a shorthand for writing the vector that is the sum |v> + |w>

@DanielSank I don't know what that means

DanielSank

github.com/DanielSank/FourierTransform

@0celo7 Why do you keep posting excerpts? Are you making fun of me or what?

gtg for a minute

0celo7

@DanielSank No, but that statement is not good

when you start labeling kets by eigenvalues, that's wrong

ACuriousMind

21:23

@DanielSank I think he wants me to fight you over your notation :P

0celo7

^ ...perhaps

Danu

Ocelot, always trying to stir up trouble... ;)

0celo7

that's why you love me

Slereah

You know, when I was in school my math teachers were always really insistent

YOU MUST PUT THE ARROW ON THE VECTOR

Nowadays I realize that math people don't give a shit

Danu

Mar 1 at 18:48, by ACuriousMind

I don't love you, and what little brainpower I had available today has been drained already, so I'd prefer not to think hard in the next hours

0celo7

21:25

he was hungover when he said that

he didn't mean it

Danu

(incoming...)

ACuriousMind

@Danu No, I can't bear to see his little heart break.

0celo7

@DanielSank I don't know how to use GitHub!

Ahhhhhhh! I have comments!

I don't know where to put them!

John Duffield

I thought I might write another book. Using my stack exchange answers to help out here and there. I also thought I might have a chapter or two about physicists and the state of physics.

0celo7

lol

John Duffield

21:29

What was that about being nice?

0celo7

@ACuriousMind What are you saying

@JohnDuffield I'm nice :)

@Danu Chap. 9 of BLT.

@ACuriousMind Ok, my life is over. I just sent a snap containing just "huh?" to Rebecca. I'm an addict

why did you do this to me

Slereah

Who is Rebecca

0celo7

your mom

Slereah

That is not my mom.

John Duffield

Anyway, I was thinking of stuff like this, but more so. Thoughts?

Slereah

21:35

You might have the wrong mom.

Be careful it is not your own

0celo7

@Slereah step mom?

Slereah

Also no

I have a step dad, but he is not called Rebecca either

0celo7

heh

ACuriousMind

@0celo7 What did I do? You started saying it.

0celo7

@ACuriousMind ever since you pointed it out I can't stop

@ACuriousMind in one line, what does the Feynman propagator mean

Slereah

21:37

It's a time symmetric propagator

ArtOfCode

a what now

0celo7

if you had to explain to someone why you want to calculate it

in one line

ACuriousMind

@0celo7 wat

0celo7

what would you say

Slereah

It's a propagator where the integration contour goes between the poles

0celo7

21:38

sigh...

Slereah

Well you asked

ACuriousMind

@0celo7 It's the probability amplitude for a particle to go from x to y. (True enough to shut them up :P)

Slereah

But then that is also true of the retarded and advanced propagator!

0celo7

OK, I knew that, but I thought it was "wrong"

ACuriousMind

@0celo7 It's true in usual QM and free field theories, and false in general QFT

0celo7

21:39

@ACuriousMind why is it wrong in interacting theories?

Slereah

Because for a start there's no particles in QFT

0celo7

is it true of the corrected propagator?

ACuriousMind

What Slereah said, you can't even define the notion of particle properly.

Slereah

It is even impossible

0celo7

@ACuriousMind so what does it mean then

Slereah

21:40

There's theorems and all

0celo7

@ACuriousMind I'm still not convinced of that, but whatever

ACuriousMind

@0celo7 It's the Green's function for the classical equation of motion. It "propagates" a given source/disturbance through the field

Slereah

If you assume the usual Hilbert space structure and Lorentz invariance, you can't have a notion of particles

0celo7

@ACuriousMind Ok, we're doing that thing were you're saying things I know and my question isn't precise enough

Slereah

Isn't the Green function the other one

The... Dyson function?

there's like 7 different contour integrals in QFT

I can never remember which is which

ACuriousMind

21:42

@Slereah Yeah, it might not be exactly the "Green's function", but close enough, we're physicists!

Slereah

To give you a rigorous mathematical explanation, the contour integrals are : Above contour, below contour, 'round the pole contour, 'round the other pole contour, in betweeny contour, 'round both poles contour and 'round both poles contour but doing a figure 8

0celo7

haha

Slereah

Above and below are retarded and advanced

Feynman is in between

the others are the... non-green function ones, I think?

Emilio Pisanty

Any mods around? @DavidZ, @Qmechanic?

Slereah

Like just solutions of $D\varphi = 0$

0celo7

21:44

I'm not sure my examples of applications of Fourier transforms should come from QFT, now that I think about it

ArtOfCode

@EmilioPisanty Does it need to be a Phys mod?

ACuriousMind

@EmilioPisanty I see @dmckee lurking

0celo7

@ACuriousMind Are Fourier transforms used in Riemannian geometry?

I've never seen it.

Emilio Pisanty

@ACuriousMind Naw, last seen an hour ago

Slereah

I've seen generalizations of the Fourier transform used in Riemannian geometry

It's called the...

Emilio Pisanty

21:46

@ArtOfCode Would be preferable but maybe you can help

Slereah

Hm do I have it somewhere

ArtOfCode

@EmilioPisanty Try me :)

Emilio Pisanty

Or maybe even a neutral look would help more.

ACuriousMind

@0celo7 Geez, I'm not your personal math encyclopedia. Google "Fourier transform Riemannian geometry" :P

0celo7

@ACuriousMind that never occurred to me.

ACuriousMind

21:47

I honestly don't know if you're joking oO

user54412

ACuriousMathopedia

0celo7

@ACuriousMind I'm actually not.

Ok, so I'm going a math presentation, I guess. I need to learn how to use the LaTeX presentation thingie

What's it called?

ACuriousMind

beamer

0celo7

And how do I import the official school PP template into Beamer?

Slereah

"Exact QED Path Integration of the Maxwell Action, with Gravitational Curvature and Boundary Terms, Using Pontryagin Duality"

Ah, that's the one

Pontryagin Duality

0celo7

21:49

That's some topological group thing

@ACuriousMind Basically, I need all the examples for applications of Fourier transforms

Morse theory?

ACuriousMind

@0celo7 Good luck with that

Slereah

Well then maybe take classical examples of it

0celo7

My classical examples are QFT

Slereah

Fourier transform is gonna be mostly solids, EM, heat equation

Shit like that

QFT also yes

0celo7

I'm gonna do a lot of QM

Slereah

21:50

Anything linear really

Oh electronics also

0celo7

But I don't think any of the undergrads have taken a formal QM course -.-

@Slereah don't know shit about that

Slereah

@0celo7 is gonna be the worst fucking student

0celo7

huh?

Slereah

He's gonna be all UH ACTUALLY PROFESSOR THAT'S NOT PART OF THE HILBERT SPACE

ACuriousMind

@Slereah I have never done that. No. Definitely never...

0celo7

21:52

@Slereah mb I should take the functional analysis QM course before the physics QM course

Slereah

greensfunction.unl.edu/home/index.html

0celo7

::gets out Shankar::

::finds multi-line equations::

So this is why scattering sucks

Has anyone seen the Canadian kid recently?

ACuriousMind

@0celo7 You mean @HDE226868? ;D

0celo7

@ACuriousMind No.

Slereah

Canada On Strike Song

►

ACuriousMind

21:59

@0celo7 Wouldn't be the first Canadian to disappear from this chat, I've not seen Jim in ages, either

0celo7

Do they freeze to death or something?

Transcript for