@ACuriousMind can you Fourier transform a differential form?

and do anything cool with it?

@0celo7 Have you tried to google that?

Uhhhhh

Yes.

Good, because I have genuinely no idea

::shock and horror::

@EmilioPisanty Well, now that I've been pinged I'm more or less around. Have to go soon, though. I've orders from my better half.

@EmilioPisanty : Yes?

a differential form is just a fancy tensor

As long as it's linear you can Fourier transform it

I need some help, more on chat.stackexchange.com/rooms/36669/…

@Slereah I don't think so

The Fourier transform relies deep down on Poyntragin duality, which needs the thing your function lives on to be a topological group, but not all manifolds are topological groups

@Qmechanic You'll find you have a ping about it in TL, though there's not much more info in there.

In other terms, I have doubt that the Fourier transform is well behaved with respect to the transition functions on chart overlaps

@ACuriousMind Well in Minkowski space, I mean :p

@ACuriousMind No fight. Love.

Or $R^n $

@Slereah That should work

@DanielSank <3

Ok what the shit

You love @DanielSank but not me??

Although I'm sure that someone somewhere made a paper

THE GENERALIZED FOURIER TRANSFORM ON RIEMANNIAN MANIFOLDS

THE GENERALIZED FOURIER TRANSFORM ON PSEUDORIEMANNIAN MANIFOLDS

THE GENERALIZED FOURIER TRANSFORM ON DEGENERATE MANIFOLDS

wth is a degenerate manifold

THE GENERALIZED FOURIER TRANSFORM ON TOPOLOGICAL SPACES

ok calm down

THE GENERALIZED FOURIER TRANSFORM ON SETS

THE GENERALIZED FOURIER TRANSFORM ON LOGICAL WELL FORMED FORMULAS

...

Then again, I've seen papers on derivatives for boolean logic

THE CATEGORY-THEORETIC FOURIER TRANSFORM

So who knows!

@ACuriousMind sigh...

Why are we using all caps, btw? :D

It sounds more important that way

@ACuriousMind why do you hate me

@0celo7 I don't hate you.

you said you don't love me

Affection is a continuous spectrum, not a binary choice :P

I wonder what's the oddest math mash up I've ever seen

@ACuriousMind let me have this dichotomy

Oh wait

There was that paper on general relativity and computability theory

I think I misused that word.

I don't care.

Because ACM doesn't love me, life is not worth it

@Slereah huh?

@0celo7 currently

@0celo7 arxiv.org/ftp/math/papers/0209/0209332.pdf

@Slereah :(

actually, me right now:

@ACuriousMind </3

I'll never ask you about math again

sniff

Me right now :

how do you find this crap

stop taking so much LSD, then

@Slereah Pass the LSD, then

Well that certainly helped Francis Crick

@ACuriousMind you're avoiding me

I want to know this too

I think they're just there to mock me

Because that's what happens when you integrate linear things?

Also quadratic things are invariant with things

$x \rightarrow -x$

If it was linear it would not be invariant by parity

@ACuriousMind no, $|\psi|^2$ is really $(\sqrt{\psi^*\psi})^2$

Well $\psi \psi^*$ is a

product

A lot of things are product

Because those are full of symmetric goodies

ok, I propose a new question

"why are there products in physics"

why $\mathrm{i}\hbar$ and not $\mathrm{i}+\hbar$

Dimensional analysis

why $8\pi G$ and not $8+\pi+G$

Dimensional analysis is a thing they teach you and then you pretty much never use it again

<3

@ACuriousMind ::cries::

You love HIM

but hate ME

@0celo7 Lol, that's a "bless your heart" style '<3'

have you done battle with him before?

@0celo7 I think so. These users keep changing their names :P

Anyway, another one for the fan club

I'm the president...

@ACuriousMind basic QM question:

if $\psi$ is sharply peaked around $k=+k_0$ in $k$-space, why is $$\int_\mathbb{R}\mathrm{e}^{\mathrm{i}k_1x}\theta(-x)\psi(x)\mathrm{d}x=0$$

(approximately)

is it because by Parceval or whatever this would be an inner product on $k$ space

and then the exponential and wave function don't overlap?

but that doesn't make sense, because $\mathrm{e}^{\mathrm{i}k_1x}$ is a positive momentum eigenstate, right?

@ACuriousMind Please, this has confused me for two years now

physicsforums.com/threads/…

Me wondering about this two years ago ^

@0celo7 That there is the Fourier transform of $\theta\cdot\psi$ evaluated at $k_1$. By the convolution theorem, this is the same as convolving the Fourier transform of $\theta$ with the Fourier transform of $\psi$. Now the Fourier transform of $\theta$ is a $\delta$ with some complex constant added behind it. Convolving that with $\psi$ gives $\psi(0) + \text{const}F(\psi)(k)$, and if $F(\psi)$ is peaked around $k_0\neq 0$ and $k_1\neq k_0$, that's zero at $k_1$.

(at the physicists level of rigor, the actual proof is probably more bothersome because the $\theta$ is a distribution)

Well I have no clue what you just said

what the hell is $F(\psi)$

The Fourier transform of $\psi$

Have you done convolutions yet, @0celo7

Sorry, just picked a notation for that :D

@Slereah yes?

Ah, the $\psi(0)$ in there should be $F(\psi)(0)$.

why?

Because you have to convolve $F(\theta) = \delta + \text{const}$ with $F(\psi)$.

Shankar says it's because $\psi$ is orthogonal to negative momentum eigenstates

I took that to mean $\mathrm{e}^{\mathrm{i}k_1x}$ is a negative momentum eigenstate, but that seems wrong

because it's not

@ACuriousMind It would appear the FT of $\theta$ is $\delta(k)+c/k$.

not a constant

Oops. Still, the argument works.

I don't see how

Away from the peak, $F(\psi)(k)/k$ will still be zero, right?

I don't know

oh, that's just $\psi$ in momentum space, yes

@ACuriousMind : it takes two to tango. When you detect a photon at slit or a screen wavefunction interacts with wavefunction. Hence $\psi^2$.

lol

@0celo7 Well, I take "sharply peaked around $k_0$" to mean that $F(\psi)(k)$ falls off to zero very quickly away from $k_0$

@ACuriousMind yes, yes

I'm a bit puzzled what the $-$ in the $\theta$ is supposed to do, though

ah and $F(\psi)(0)=0$ too, got it

@ACuriousMind he wants to split the wave function into a part to the right and to the left of the potential

I'm looking at scattering shit for my presentation

@0celo7 Ah, okay, it has to do with the physics he considers, alright ;)

Ok, now to prove $F(\theta)(k)=\frac{1}{2}[\delta(k)-\mathrm{i}/\pi k]$

apparently that's hard

and the author did not mention it anywhere

so I'm still confused @ACuriousMind

@0celo7 : your repeated lol comments are not in accord with the be-nice requirement. Your use of expletives isn't good either.

oops :)

@0celo7 Just a moment, I will see if I can "prove" that in a quick way

Very funny. Not. I'm off to bed.

@ACuriousMind Ok, but I'd rather understand the way the book wants me to understand it.

It should be pretty intuitive.

@0celo7 Well, that I don't know

@ACuriousMind if you read the stuff in the link, I quote the book directly

I would appreciate it if someone could explain-to-OP/mediate/step-in/vote-to-reopen/vote-to-close here.

@ACuriousMind Yeah, he says that the position space rep of the state $|p\rangle$ is $$\psi_p(x)=\frac{\mathrm{e}^{\mathrm{i}px/\hbar}}{\sqrt{2\pi\hbar}}$$

so that's the positive momentum eigenstate

@ACuriousMind and $k_0\ne k_1$ is not necessary.

@Qmechanic I left a comment

@ACuriousMind apparently we can ignore the $\theta(-x)$ factor since $\psi(x)=0$ for $x>0$

@0celo7 oO

@0celo7 oO

@ACuriousMind do you just want the page :)

@ACuriousMind : Thx.

Shankar is on Springer

@Qmechanic btw, please tell me if I don't leave the types of comments you had in mind!

@0celo7 Yeah, tell me, and then give me a bit of time to think about it

@ACuriousMind It starts on page 167. Second edition.

I also need to finish this email I started writing an hour ago :D

@ACuriousMind I've gotten really good about just sending emails, don't even give them any thought

Not like that 't Hooft email which took days

@0celo7 It's not that I'm agonizing over it, I just keep doing other things

@ACuriousMind ah

The other day my advisor sent me an email with literally one symbol

I like his approach

@ACuriousMind Aha!

That reminds me of a Norbert Wiener anecdote

If $\psi(x)$ is sharply peaked at $k=+k_0$, where is $\psi^*(x)$ peaked?

Apparently Wiener and another fancy mathematician were in a classroom

Both very deeply in thoughts

@0celo7 $-k_0$

@ACuriousMind Cool beans.

And on the blackboard, there was only one symbol

Like

~

And to this day, nobody knows what that was about

@ACuriousMind So $\mathrm{e}^{\mathrm{i}k_1x}$ is really the conjugate of something peaked at $-k_1$!

@0celo7 Yeah, now that you say it, that's what he means, and the inner product is $\int f^\ast g$, after all.

and when we talk about Fourier shit we have to take conjugates on one of the factors

@ACuriousMind Only took me 2 years :D

I feel like I should somehow make this into a PSE post

@dmckee Would you happen to know how to import a PP template into beamer

...I don't think you can do that

So should I just not use beamer?

But some TeX wizard might have written something for that, so I'm not sure

Your university does not provide a TeX template?

Nope

Barbarians

I wonder if the math department has one

that they hand around

@ACuriousMind I talked to the grad students in my lab about it

they say Word and PP are so much easier to use, so that's what everyone uses

(in our field)

@ACuriousMind @dmckee whom should I email/talk to about getting the TeX template?

Lang will just say "use the Word equation editor"

but if I'm doing an hour on Fourier transforms I don't want to spend 20 hours formatting equations

I don't think there will be one if the university does not provide it, but you said it already - I'd try the math department

the math department is pretty big

I found a dissertation template for TeX

holy shit is this a joke

you can't actually submit your thesis in LaTeX

@0celo7 While beamer supports the notion of templates, the existence of official version is limited at best. Most of the "templates" you'll find will be the work of some individual, and they are generally not updated.

that can't be right

oh

At my grad school your submission was paper not a file. I hope that is getting rarer these days.

the university does not guarantee that the template provided below meets the current standards

so you have to adjust the TeX one to meet the "official" Word one

I just downloaded a tex file from the math department

I guess tonight will be me figuring out TeX

@dmckee do you know of a good guide on how to use beamer?

@dmckee I had to provide three printed copies of my bachelor's thesis in addition to a disk with the PDF file on it.

@0celo7 The official documentation is pretty good.

And I think the number of copies only grows for master and PhD

My dissertation required six. Three for the library, two for the department and one for me. I did several spares so I could give one to my advisor and one to my dad.

The department has a big shelf of them in the conference room, but only one of each. I don't know what they did with the other departmental copy.

@dmckee TeX or typewriter? ;)

(I don't actually know when it became common to set papers in TeX)

TeX, but the required format dated from typewriter days. Section headings in all caps. Chapter headings in all caps and underlined. That sort of thing.

I actually rigged the tex so that it could produce two outputs. The school's format was just shy of 200 pages. The tree-friendly format was 110, so 55 if printed double-sided (which wasn't allowed for the school's format!).

@0celo7 I think I actually didn't conform to the standard formatting set for title page and abstract. No one cared.

But I'm generally a bit surprised how little they seem to care about formalities here at times

@ACuriousMind Wow. Our margin-lady was nice as anything, but very strict. She really did have a steel ruler marked in 16th of an inch to check things with.

@dmckee what's that

She was interested in typography, so we had a couple of very interesting email exchanges about the way TeX did things.

@0celo7 google.com/search?q=beamer+documentation

First link.

> Für alle, die die Schönheit von Wissenschaft anderen zeigen wollen.

Damn Germans are everywhere

Notice the "HowTos" in chapter V.

@dmckee Well, it might be that they are more strict for master's and PhD theses. They generally treat the recent Bologna split of the former diploma into bachelor and master as an annoyance

@ACuriousMind Ah, I didn't end up needing a joke today

He found my German with a Texas accent pretty funny

@dmckee aha! found a template on the UTK math dept. website

ERROR

@0celo7 ::sniff:: ::sniff:: Our little guy is learning to do things for himself. Anyone have a hanky?

HELP

@0celo7 Don't load hyperref explicitly when using beamer.

what is hyperref?

The package that makes it so you can click on stuff e.g. in the table of contents so you can jump to sections?

I'm not loading that

I don't even know what it is

@0celo7 Find the option (either to the class or to a package) where postscript is being specified and turn it off. Or ever set pdf or lau explicitly.

I don't know what any of those words mean

That's a fairly old template that expects you to run latex and dvips to end up with postscript.

Do you see a dvips anywhere in the template?

Probably in the options to some usepackage

^ That. Probably near the top.

not found by the search function

anything with dvi in it?

Ask someone in the math department whose hair is not white or missing.

math.utk.edu/~msaum/papers/prestips.tex

that's the file

Got this message: Daily vote limit reached; vote again in 5 minutes. :)

It's just about midnight in Greenwich.

@0celo7 Okay, I found the issue within 2 seconds of opening the file. Look closer.

@ACuriousMind where

I don't need that hanky anymore.

I'm so confused

is there a typo or something?

what do I do?

@ACuriousMind oh come on please just tell me what to do