The h Bar

ACuriousMind

18:00

@Bass Take the classical field to be complex-valued. Then Hermiticity is $\phi = \phi^\ast$.

(at all points)

Bass

@ACuriousMind so it's real-valued? It's imaginary part is zero everywhere?

ACuriousMind

@Bass Exactly

Bass

Strange terminology.. Does it stem from the QFT side where the analogue is the hermiticity of operators? If not, why not just say "real field"?

0celo7

@Danu hey buddy

don't laugh at me

ACuriousMind

@Bass People do also say "real" and "complex" field.

0celo7

18:08

just ignore that

Danu

Nov 10 at 15:59, by 0celo7

@Danu The ol' I can't figure out this test problem no one wants to help me and people laugh at me and are too smart and I'm going to class

Bass

@ACuriousMind ok thanks!

DanielSank

Did another problem last night. Did you know that the Poisson distribution has the same value for all cumulants?

Bass

@ACuriousMind is the QFT operator $\hat\phi$ hermitean if and only if the "underlying" classical field $\phi$ is real?

ACuriousMind

@Bass Yes

Bass

18:15

Ok cool

Huy

i.imgur.com/cnNuLEk.jpg this is some interesting textbook

0celo7

seems legit

Danu

Does anyone know a neat derivation of the identity for the discrete Fourier transform of the Dirac delta "function":

$$ \sum_{n\in \mathbb{Z}}e^{in(x-x')}=2\pi \delta(x-x') $$

?

Mostly: I forgot how to take the discrete Fourier transform; HALP :P

ACuriousMind

@Danu Same as for the continuous case - do the inverse transform and observe both sides agree.

Danu

@ACuriousMind I realized as soon as I posted, hence the second comment :P

ACuriousMind

18:22

@Danu I see :D

0celo7

@Danu Any decent engineer would know that...

Danu

@0celo7 Right, get on it then

ACuriousMind

Geez, Emilio and Kyle don't get along well :P

Danu

@ACuriousMind Linkerino?

0celo7

@Danu I'm a terrible engineer :(

ACuriousMind

18:26

@Danu Comment thread to Emilio's question

0celo7

@Danu slinkerino

Danu

I think @KyleKanos misses the petty fighting of the h bar and fulfills his needs elsewhere ;D

0celo7

petty fighting

you're the only belligerent one

ACuriousMind

::snorts::

0celo7

@ACuriousMind pig

skull petrol

18:28

::chuckles::

ACuriousMind

::slaps @skullpetrol:: Nothing to chuckle here, we're a serious chatroom.

0celo7

violence now??

skull petrol

:(

NeuroFuzzy

So I have a question which full disclosure is part of a homework problem I'll be graded on. A balloon in a vacuum, temperature T/pressure P has a hole area A in it. What's the force on the balloon? Or rather, why ISN'T the force just $PA$? I can use the maxwell distribution to find the average outgoing momentum is $PA/2$ but the question wants a second way too.

0celo7

I vote to close this chat post as off-topic for reasons of homework phobia.

ACuriousMind

18:31

Please see our meta for further guidance.

skull petrol

Don't beat me...master :P

0celo7

> (~12:30 gmt to ~11:00 gmt),

What

He's at work for 22.5 hours o.o

ACuriousMind

Yes, that's exactly what that means :P

Danu

physics.stackexchange.com/review/first-posts/105850

wat do?

0celo7

wow no wonder why he doesn't come here...

ACuriousMind

18:33

@Danu ...you clicked No Action Needed?

gert please let me know what is anti gravity paint? — Amal Babu 14 mins ago

When snarky comments backfire...

Danu

@ACuriousMind I did? Woops... I wanted to click "skip"

ACuriousMind

-3

A: How come gas molecules don't settle down?

Gas molecules don't settle down because they're like men - afraid of commitment. Men are from Mars originally, however Venus women divorced every single Martian after constant complaints that they felt unloved, and that no one ever listened to them. They were awarded the Red planet in a landmark ...

I lol'd

Danu

I was really close to VTC'ing but I didn't really know what to VTC for :P

@ACuriousMind Niceeee

0celo7

They do settle down...

Poincare's theorem!

For a little bit at least.

ACuriousMind

@Danu Well, now you completed the review, instead :P

Danu

18:37

@ACuriousMind Life is life

skull petrol

When do you plan to take statistical mechanics @0celo7?

0celo7

@skullpetrol Uh

ACuriousMind

@Danu Na-naaa-na-na-na-a

0celo7

I'm not taking a course on it per se

You get a lot of it in various NE classes...

skull petrol

I see.

0celo7

18:39

I could take a class on it...

Don't know when

wonder what the prerequisites are...

skull petrol

How about thermodynamics?

0celo7

I have an intro next semester

Then the actual course next fall

It's the one all engineers take from the mechanical department

Stat mech requires 231 which is intro E&M

So I could take it starting next spring

But that's already my crazy 20 credit hour one

skull petrol

Ok.

NeuroFuzzy

@0celo7 you could take it now and help meee

:P

Danu

Yo forreals though, I can't derive that discrete FT thing.

NeuroFuzzy

18:43

get a prof to sign off on it! No prob! Hehe.

Danu

How does taking the inverse discrete FT help, @ACuriousMind

0celo7

@NeuroFuzzy nah it's thermo for physicists + intro stat mech

nothing you couldn't figure out :P

Danu

@0celo7 What's the norm for credits/semester?

NeuroFuzzy

@0celo7 I can't figure out a hole in a balloon so...

0celo7

@Danu 12 is full-time student

15-16 is the average

19 is the maximum without approval from the department head

Danu

18:44

15-16 average? k

0celo7

PHYS 551 - Statistical Mechanics

3 Credit Hours
Ergodic theory, classical ensemble theory, quantum mechanical ensembles, relation of statistical mechanics to thermodynamics, transport theory and approach to equilibrium, phase transition, fluctuations and correlations.
(RE) Prerequisite(s): 521, 531, and 571.

@NeuroFuzzy That sound like what you're doing?

Danu

The point system here is different. 30 is the norm.

NeuroFuzzy

@0celo7 Yep! Roughly the first 45 sections of landau and lifshitz statistical physics

Danu

How much do you do per semester @ACuriousMind?

I assume a lot, since you know a lot more than me, haha

0celo7

@NeuroFuzzy Well the prereqs are QM1, Analytical Mechanics and Math Methods 1

So I probably won't take that any time soon

NeuroFuzzy

18:46

@0celo7 rats.

0celo7

PHYS 571 - Mathematical Methods in Physics I

3 Credit Hours
Linear vector spaces, matrices, tensors, curvilinear coordinates, functions of a complex variable, partial differential equations and boundary value problems, Green’s functions, integral transforms, integral equations, spherical harmonics, Bessel functions, calculus of variations.
Cross-listed: (Same as Mathematics 517.)

Recommended Background: Advanced calculus and differential equations.

"tensors"

I think they mean index gymnastics

ACuriousMind

@Danu Take the $\delta$ and apply the inverse transform to it. The result should be unity. Then observe that your original thing was to show that the transform of unity is the delta, and by bijectivity of the Fourier transform, you have then shown that, too.

Danu

@ACuriousMind Try deriving that the result is unity.

Also it's not the usual delta, but a "periodic" one.

ACuriousMind

@Danu Between 32 and 40 thus far. Nearly nothing this semester because there wasn't much interesting.

0celo7

@Danu Do you want the solution

ACuriousMind

18:49

What's a "periodic" delta?

Danu

@0celo7 Sure

0celo7

It's in Cahill

Danu

@ACuriousMind Who knows

It's in Luest's book, and I need it to derive the commutators for the string.

0celo7

@Danu Page 97 ff. of Cahill

Danu

but he states the formula without proof.

NeuroFuzzy

18:49

@ACuriousMind What does that mean? Credit hours?

Danu

@0celo7 Neat.

0celo7

@Danu Yup!

I remember grabbing Cahill for that section :)

ACuriousMind

@NeuroFuzzy Yeah, but in the European system. 30 is the norm, as Danu says

0celo7

btw it's not rigorous

but maybe it can convince you

Danu

It's not really the same thing, is it?

NeuroFuzzy

18:50

@ACuriousMind oh I missed Danu's message

0celo7

@Danu the thing in cahill?

ACuriousMind

@Danu I hate physicists :P

0celo7

of course it is

the Dirac comb is exactly what you're looking for...

top of page 99

ACuriousMind

Let's see...If we are on an interval $[0,1]$, the Fouier transforms live on $\mathbb{Z}$...

0celo7

you take the fourier series

Dirac comb

In mathematics, a Dirac comb (also known as an impulse train and sampling function in electrical engineering) is a periodic tempered distribution constructed from Dirac delta functions for some given period T. The symbol , where the period is omitted, represents a Dirac comb of unit period. Some authors, notably Bracewell as well as some textbook authors in electrical engineering and circuit theory, refer to it as the Shah function (possibly because its graph resembles the shape of the Cyrillic letter sha Ш). Because the Dirac comb function is periodic, it can be represented as a Fourier series...

This is what you need.

I don't know why you say it's not the same...

Danu

18:53

Oh that's page 99 I think

0celo7

2 mins ago, by 0celo7

top of page 99

:(

ACuriousMind

@Danu: It works when you know what the correct inverse transform is ;)

Danu

@ACuriousMind Ba-dum-tssss

0celo7

@Danu are you convinced or...

ACuriousMind

I guess you tried using the sum just with minus signs in the exponent?

Danu

18:56

@ACuriousMind "using"...

I wrote it down and saw no simplification

ACuriousMind

Yeah, no, the inverse is an integral, the two transforms are not as symmetric as on $\mathbb{R}$,

Danu

@0celo7 Convinced sure, but I don't wanna write a "derivation" like that.

@ACuriousMind Ah...

I told you I don't remember how to do it :P

I feel like I must've learned this though, at some point.

ACuriousMind

Because one transform goes from functions on $[0,1]$ to functions on $\mathbb{Z}$, and the other in the other direction.

0celo7

where would you learn this

real analysis?

complex?

Danu

mathematics for physicists

lol I never took any analysis course

0celo7

18:58

oh

so Phys 571 in my case

Danu

well I took complex analysis (for physicists)

0celo7

"integral transforms"

Danu

@ACuriousMind So errr what is the inverse?

0celo7

@Danu why

even engineers take analysis

Danu

@0celo7 Because I don't need it.

0celo7

18:59

@Danu one can do measure theory without analysis?

Danu

@0celo7 I don't need measure theory.

0celo7

@Danu you can do functional analysis without measure theory?

Danu

I need basic facts about measures, and perhaps about functional analysis

I don't care for the nitty-gritty---I'm much more geometrically-minded.

ACuriousMind

@Danu One is $L^2(\mathbb{Z})\to L^2([0,1]), f(n)\mapsto \hat{f}(x) = \sum_n f(n)\mathrm{e}^{-\mathrm{i}nx}$, the inverse is $L^2([0,1])\to L^2(\mathbb{Z}), g(x)\mapsto \tilde{g}(n) := \int_0^1 g(x)\mathrm{e}^{\mathrm{i}nx}\mathrm{d}x$, possibly with factor of $2\pi$ missing because I'm a lazy fuck.

Danu

The basic facts are simple to learn yourself once you know enough

@ACuriousMind Nevermind the $2\pi$ haha

0celo7

19:02

@Danu ok

Danu

Also yes you can do functional analysis without really knowing measure theory, btw.

0celo7

I'll take your word

ACuriousMind

Let me try to prove those are inverse to check I haven't lost my mind.

0celo7

@Danu really

the functional analysis book my school uses opens with a review of measure theory

Danu

Not professionally as a mathematician, but you can do all I care to learn just fine.

@0celo7 Haha, that was very tautological at first :D

0celo7

19:03

@Danu :)

In any case, I've been told PDEs require measure theory beyond a cursory knowledge

maybe that's a lie

Danu

Depends how much you want to know about PDEs.

0celo7

not sure yet

but it raises GDP

Danu

I'm not particularly interested yet---perhaps once I get to learn more about spin manifolds and perhaps Atiyah-Singer-related stuff will spark my interest?

0celo7

interested?

in?

Danu

in PDEs

0celo7

19:05

oh

a lot of engineering is secretly a PDE

so having a solid background in PDEs is good

ACuriousMind

Damn, @Danu, I need your identity to prove those are inverses of each other :D

Danu

Real "mathematician-style" PDE knowledge is probably not necessary at all as an engineer.

ACuriousMind

So that way is not good.

0celo7

@Danu Probably.

Danu

@ACuriousMind Yeah I'm not getting too far either, so far

0celo7

19:07

But I'm going to do what I want

So screw all of you

ACuriousMind

Also, either the integral upper bound needs to be $2\pi$, or the variable needs to be $2\pi x$ instead of $x$.

Danu

$$\sum_{n\in\mathbb{Z}}\int \mathrm{d} \sigma' e^{i(n-m)(\sigma-\sigma')}=1$$?!

0celo7

Except you @ACuriousMind

Danu

@ACuriousMind Never mind the $2\pi$, I will put it in later.

I want to use contour integration

but the only remaining $n=m$ term is ehh... not nice :P

$1/0$ somethingsomething

0celo7

1/0=7

Danu

19:10

Oh wait I shouldn't be integrating over the entire real line, heh.

user685252

No @0celo7 0/0=7

skull petrol

@ChrisWhite Racial Draft

Danu

@user685252 No, listen to Mukhanov: "Dividing zero by an elliptic operator is like dividing by 5; dividing it by an hyperbolic operator is like... Green's functions!"

0celo7

@user685252 uh, no

Danu

(just wanted to pull out that quote) :)

0celo7

19:17

that's undefined

Danu

also @ACuriousMind wikipedia has a derivation

close enough

0celo7

@Danu in the link I posted

ACuriousMind

I felt the whole time something was off here...I'm not sure which link you mean but the relevant thing to use is Parseval's theorem.

0celo7

@ACuriousMind something is indeed off

@Danu is an imposter!!

Danu

@0celo7 Exactly

0celo7

19:22

@Danu you're welcome

ACuriousMind

@0celo7 huh?

0celo7

@ACuriousMind exactly.

ACuriousMind

I have no idea what you're talking about

0celo7

people say that a lot

skull petrol

Me neither.

Danu

19:24

@0celo7 :-)

0celo7

@Danu you could use physics math

when the exponential is 1 you get infinity

Danu

@0celo7 Yeah, no

skull petrol

Hey! Who divided by 0 up there :P

0celo7

and when it's not you're gonna get cancelation

Danu

I need slightly (but only slightly) more rigorous ;)

0celo7

19:25

so it's just a bunch of deltas, obviously

Skull Rigor

(removed)

skull petrol

A rigorous skull is hard to find :P

Most of 'em are just numb.

Probably comfortably numb

0celo7

19:44

I read that as conformally numb

0celo7

20:30

Chat has left this life.

Qmechanic

21:57

-1

Q: Lectures on black holes and the $AdS_3$/$CFT_2$ correspondence, Per Kraus

I have been reading Per Kraus' paper on $AdS_3$/$CFT_2$. I am struggling with deriving eq 2.16 on page 9, the $AdS_3$ stress tensor. The two metrics (conformal boundary metric and induced metric in the Fefferman expansion in page 8 (2.12)) and the radial coordinate confuse the hell out of me, I t...

Reopen? This is OP's first post. OP might not know how to TeX. Perhaps someone could help improve the post?

Slereah

Been playin' Fallout for 10 hours

Welp

ACuriousMind

@Qmechanic Don't reopen in the current state, I'd say, but I'll see if I can edit it.

0celo7

@Slereah Should I buy it when I get home?

Slereah

It's alright

Some good some bad

Milquetoast answer right there

0celo7

22:17

what kind of answer?

@ACuriousMind just saw myself floating in from the top

Qmechanic

22:39

@ACuriousMind : Thanks.

0celo7

@ACuriousMind Are you going to get F4?

Slereah

Though I would say this at least

Maybe wait until it is patched a bit

Nothing game breaking but there's a few little bugs

ACuriousMind

@0celo7 Not soon, what I've heard and read so far doesn't sound like a particularly amazing improvement over the other games. Also, one should always wait the first few patches with Bethesda

Slereah

Mostly it's pretty minor stuff but annoying

Sometimes you fet stuck, sometimes the screen isn't properly centered, the followers get a bit lost sometimes

Also as a general comments on Bethesda games

Bethesda calm down with the random objects

Now you basically HAVE to pick up random objects

0celo7

what

Slereah

22:53

the crafting system is based on a whole bunch of components

Most of them you basically have to get from random objects

Combined with the usual inventory problems this is getting a bit out of hand

Calm your tits Bethesda

I know you want to evoke a nostalgia of the retrofuturism of the 50's but that doesn't mean I have to pick up every nuclear powered razors in the world

Alfred Centauri

23:21

@ACuriousMind the knowing is not nearly as enjoyable, for me, as the learning or the discovering. I suppose that's the primary reason I find myself a physics grad student at the age of 55.

Slereah

23:43

Judging Fallout 4 (Judging by the Cover)

►

:D

0celo7

why did you send me that

now I gotta spend monies on this game

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