The h Bar

Slereah

5:00 PM

I cannot parse that sentence

David Z

Our time for the official chat session is about up, but feel free to keep going. See everyone in two weeks!

I'm off to bed :-P

bolbteppa

Thanks for answering

yuggib

@DavidZ good night ;-)

@bolbteppa again, thanks for the interesting questions

0celo7

@yuggib check "canonical quantum general relativity"

yuggib

I have no problem continuing to chat for a while more if you want

user116211

5:01 PM

@yuggib, Amazingo

0celo7

It's LQG in AQFT language

yuggib

@0celo7 yeah, it is Thiemann as well

I tried to read his CMP paper "On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories" (also with AQFT language)

Slereah

@0celo7 The horror

yuggib

but I was not able to follow

Slereah

Did you try any low dimensions QG theories, maybe

Those are usually easier to define

ACuriousMind

5:03 PM

@Slereah String theory does not ;)

Slereah

Well yes

It's on a fixed background

yuggib

not really...but as I said I was interested in LQG because I read that their problem is that the open question is whether general relativity is reproduced in the classical limit

so I thought I could say something meaningful about that

but I could not find a language that I could understand

Slereah

Also what do you think of using Colombeau algebra to do non-free QFTs

Great idea or greatest idea

yuggib

@Slereah I don't know Colombeau algebra

Slereah

It's an algebra of distributions

yuggib

5:05 PM

but there are people working on defining rigorously products of distributions

not far from you

Slereah

Tell him to hire me

yuggib

check his works

and contact him ;-)

he's a nice guy as well

Slereah

I guess I could try~

I do have the idea of trying to do some QFT with Colombeau algebras

It's not a novel concept, there has been a few papers on that

But not that many

Since Colombeau algebras are a pretty recent development

yuggib

they do products of distributions

but I don't know if they use exactly that language

Slereah

Well there are different ways to do products of distributions

yuggib

5:08 PM

I know

Slereah

Although because of the what's his name theorem

All of them are terrible

yuggib

that's why I am saying that you should check what they did, for I am not an expert ;-)

Slereah

Schwartz impossibility theorem?

yeah

yuggib

well the AMA was not bad in the end...I feared some much more technical questions

;-P

@0celo7 was my book suggestion useful?

I have to say that I have not read his introductory book, but I know his other books and I like his style

@0celo7 I find his "Fourier analysis on groups" very nice

Slereah

Would have been here sooner but I was stuck in transport

yuggib

5:15 PM

@0celo7 and abstract harmonic analysis (i.e. harmonic analysis on locally compact Abelian groups) is probably something that you may find interesting ;-)

@Slereah No problem

you closed the session ;-)

there were a couple of good questions on the comments of the introductory meta post, but the two guys did not show up

0celo7

@yuggib Rudin?

yuggib

@0celo7 yep

0celo7

My advisor hates Rudin

He likes pictures

Slereah

Is it @Secret

yuggib

and are the two things (Rudin & Pictures) mutually orthogonal?

0celo7

5:18 PM

No, his pictures are much better.

@yuggib he has Rudin's functional analysis book

yuggib

@3750 Your question about doing math and then a PhD in physics is interesting, for it is something that always surprised me a little

0celo7

@yuggib Rudin has zero pictures.

user218912

@yuggib that's kind of what I'm doing now.

user218912

I'm beginning my bachelors of math in the fall.

yuggib

really I don't know anybody who did that cursus

user218912

5:19 PM

wondering if I should switch back to physics.

user218912

because I switched out 0.o

yuggib

and my guess is that you will struggle with physical intuition when it comes to later times

user218912

I already have no physical intuition.

user218912

xD

user218912

also

user218912

5:20 PM

what if I do a math major with a physics minor?

yuggib

of course physicists may struggle with math rigor, but I think that rigor is easier to later build up than physical intuition

@0celo7 many functional analysis books have zero pictures

@3750 I don't know, maybe it works out

0celo7

@yuggib I know

He dislikes Rudin's analysis books.

Not functional analysis

yuggib

ah...strange stance

0celo7

Why

You find everything he does strange

yuggib

I mean, either you like the style or you don't

no it's not true

0celo7

5:24 PM

I think he thinks different styles are appropriate for different subjects

yuggib

when he made you do the case $n=1$ instead of the trivial $n=0$ in that induction proof I agreed with him

@0celo7 I see

0celo7

@yuggib but he is a geometer so you disagree with him fundamentally

yuggib

@0celo7 :-D

0celo7

@yuggib the set of things you agree on is a set of measure zero

he told me I should read Oxtoby for fun after I take his analysis class

do you know this book?

yuggib

no I don't...

user218912

5:31 PM

the chemistry book.

0celo7

no, the measure theory book

user218912

what book should I read for analysis @yuggib

user218912

introductory.

0celo7

abbott

Blind

hello

0celo7

5:34 PM

he will teach you how to prove $|ab|<|a||b|$

user218912

sigh...

user218912

you're forgetting that

user218912

that's not the only thing I can't prove...

user218912

I can't prove anything.

0celo7

hmm, do you know the de Morgan laws?

user218912

5:35 PM

yeah

Blind

area51.stackexchange.com/proposals/101085/… I don't want spam, please follow it if you lke it

0celo7

how to prove $\sqrt 2$ is irrational

@3750 how to prove them

user218912

@0celo7 I looked up the proofs on wikipedia

user218912

@0celo7 maybe.

bolbteppa

Fascinating: consider the $U(1)$ symmetry of the inner product of wave functions, $<g|f> \mapsto <g'|f'> = <g|e^{-i\theta} e^{i\theta}|f> = <g|f>$. Apply the same $U(1)$ symmetry to the Klein-Gordon action. You end up with a conserved current $j_{\mu} = \mathrm{i} (\psi^* \partial_{\mu} \psi - \psi \partial_{\mu} \psi^*)=\mathrm{i} \psi^* \overleftrightarrow{\partial_{\mu}} \psi$. Stunningly this (somehow) motivates also defining $j_0$ as an inner product

$\langle \psi_1|\psi_2 \rangle= \int_{\mathbb{R}^3} \mathrm{d}^3 \vec{x} \mathrm{i} \psi_1^* \overleftrightarrow{\partial_0} \psi_2$ so that the projection of the wave function onto the $k$'th frequency gives the $a(k)$ coefficient. Getting closer to understanding $a(k)$ finally!

0celo7

5:37 PM

@3750 do it

oh I forgot, I'm no longer helping you

user218912

wow

user218912

you big meanie.

bolbteppa

@3750 what are your issues with doing a math degree

yuggib

@3750 maybe rudin as well

or bourbaki (fonctions d'une variable réelle)

user218912

@bolbteppa how did it work for you?

user218912

5:40 PM

@yuggib what about pugh?

user218912

the introductory first year analysis course i'm taking uses pugh

user218912

should I read that to prepare?

yuggib

@3750 don't know it

user218912

I did read rudin a bit at some point and I found it difficult.

yuggib

I suppose that more or less every book is ok for an introduction

0celo7

5:41 PM

@yuggib Rudin is notoriously hard

bolbteppa

@3750 I got to ignore all the baby physics courses, I was not tarnished by thinking of electromagnetism via vector calculus or by other subjects in their rudimentary forms, only Newtonian mechanics which damaged my thinking too much, I had 2 years to focus on learning enough math so I could do physics properly and it massively paid off if extremely hard and intense and am still coping in some areas,

0celo7

why would you recommend it as an introduction

bolbteppa

but considering 99% of the physics people had extreme problems with the math being thrown into Jackson/Landau/QFT courses in later years it was immensely worth it

yuggib

@0celo7 really? I found his book on harmonic analysis pretty clear

0celo7

@yuggib you probably read it as an adult!

bolbteppa

5:43 PM

@3750 read Ross Elementary Calculus and Lay's Analysis if books like Rudin on analysis are too intense

user218912

I don't want something too basic either.

user218912

I just need to figure out

user218912

how to do proofs

user218912

first.

bolbteppa

Yeah Ross and Lay will teach you how to do proofs, specifically Lay he has multiple sections on it

user218912

5:43 PM

ok I'll check it out.

yuggib

@0celo7 but I think the style was pretty clear

despite the "age" of the reader

0celo7

@yuggib One of Zee's books is my favorite book ever and the other is not worth jack shit

Same style, supposedly.

bolbteppa

Both of Zee's books are awesome so long as you don't take either of them too seriously ;)

Still want to look at the Group one

deostroll

3

Q: Why is Avogadro's law always true?

Why is Avogadro's law always true? How and why do equal volumes of gases at equal pressure and temperature contain equal number of molecules? I know it is a fundamental principle in chemistry but I wonder how it works.

statistical-mechanics

yuggib

@0celo7 the truth is that I never read an introductory analysis book

deostroll

5:47 PM

I went through the answers...but I am still not convinced...

yuggib

of any kind

deostroll

How did avogardo come to that conclusion?

0celo7

@yuggib then why don't you say that

you are clearly not qualified to recommend one

yuggib

@0celo7 I said that I like rudin's style, so I suppose his introductory book should be nice

0celo7

@yuggib ....

yuggib

5:52 PM

you (or your advisor) do not like rudin, so be it

0celo7

I have not read it

We're using two books for analysis next semester

bolbteppa

@3750 Pugh is basically the same as Rudin, if you read Rudin on page 2 remember that insane $q = p - \frac{p^2 - 2}{p+2}$ is derived from noting that if $p$ is a lub then $p + 1 < p + 2$ implies $\frac{p+1}{p+2} < 1 \rightarrow 2\frac{p+1}{p+2} < 2$ so that $\frac{2p+2}{p+2} = \frac{p^2 + 2p - p^2+2}{p+2} = p\frac{p+2}{p+2} - \frac{p^2-2}{p+2} = p - \frac{p^2-2}{p+2} = q$ that drove me insane

0celo7

I will let you know which ones when I find out.

yuggib

@0celo7 good

so I'll suggest them to people

;-P

user218912

@bolbteppa I am really liking pugh just browsing through it.

user218912

5:54 PM

it's like rudin with more details.

user218912

I guess I'll use it while figuring out how to do proofs from lay's book first chapter.

user218912

@0celo7 watch me in 60 days I'll be a proof lord.

bolbteppa

Have a look at Ross and Lay in a library or something and go through them a bit and see how it goes

0celo7

@3750 doubtful

user218912

@0celo7 wanna bet

user218912

5:57 PM

70 days from now ask me to prove anything and if I couldn't do it then I'll buy you a book.

user218912

proof should be reasonable though.

user218912

i'm saying this because I want to be motivated and not slack off.

yuggib

@0celo7 you should give a first example of a basic proof: a constructive proof of induction

(not the involved one you quoted before)

so he'll learn more quickly

user218912

he's not helping me remember?

0celo7

@yuggib Sard's theorem is indeed quite involved

My prof was too lazy to understand the proof so he made me do it and present it on the board in his office

yuggib

6:09 PM

@0celo7 I was referring to the proof of the induction principle you posted before

proof of induction is essentially a two-liner

bolbteppa

Amazing there are now 4 votes to close on physics.stackexchange.com/q/267574/25851 when it is stunningly deep

user218912

@bolbteppa yeah I agree I don't like the divide between physics and math courses.

bolbteppa

@3750 just learn calculus of variations as fast as possible and know your calculus as close to the level of Goursat's 5 volumes as quick as possible and nothing will stop you ;)

user218912

@bolbteppa goursat's 5 volumes?

user218912

how much does that cover?

user218912

6:21 PM

I know up to and including vector analysis right now.

bolbteppa

Volume 1: Calculus, baby differential geometry, Volume 2.1: ODE's, volume 2.2: complex analysis, volume 3.1: Calculus of variations, 3.2: PDE's. Those books are insane but getting as close as possible to them as you can is going to pay off massively in the long run, if you're doing a math course with the intent of eventually doing physics then these are the best books to use for that, e.g. they are some of the few Landau references in en.wikipedia.org/wiki/Course_of_Theoretical_Physics

I guess I'll take my question to the adult physics version of this site (again)

Slereah

6:39 PM

@yuggib It's difficult to do products of two field operators at the same spacetime point in Wightman/OS QFT because of blablabla

But does the same apply for AQFT

And if so why

I recall that it do

But I'm not sure why

yuggib

@Slereah in AQFT fields calculated in a spacetime point are not in the algebra, since they're unbounded

Slereah

What about like

yuggib

and I honestly don't know much about the net of algebras that implement spacelike separation etc

Slereah

$\varphi[f] \varphi[g]$

Where $f$ and $g$ have the same support

Or something

I dunno

Not sure what I'm on about

yuggib

if they have the same support, then the usual ccr apply

ACuriousMind

6:42 PM

@Slereah Now you share the usual feeling of most of your listeners ;)

Slereah

Well I am just wondering about how you implement non-free theories rigorously

ACuriousMind

I actually understood what your issue was in this case (I don't know the answer).

Slereah

How do they define the product in Wightman, anyway?

The propagator is $\varphi[f] \varphi[g]$

Well its expectation value

But how do they define that product

It's not a trivial notion for distributions

Slereah

8:03 PM

hey

That french guy who studies products of distributions in QFT lives in Lille

And I am moving there this year

How serendipitous

Balarka Sen

@Slereah Tell me about wormholes

What's the deal with them?

Slereah

Who are you, Jerry Seinfeld?

WHAT'S THE DEAL WITH WORMHOLES

Balarka Sen

No idea who that is, but no.

Slereah

Wormholes are topologically non-trivial spacetimes

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

He's just curious.

Balarka Sen

8:08 PM

@Slereah Do we even know if the spacetime is orientable?

Slereah

Do you mean our spacetime or a wormhole spacetime

Our spacetime is probably orientable

Wormhole spacetimes can be or not be orientable

Balarka Sen

weird

Slereah

Mostly it is assumed that they are orientable

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Is the country still in shock after the loss to Portugal?

yuggib

@Slereah then you can really propose yourself for a phd

Slereah

8:14 PM

It would certainly be convenient

I don't want to move again

I guess I should read his papers, first

yuggib

@Slereah anyways, considering "viet dang" as a french name is a bit far fetched

Slereah

There's a lot of Nguyen in France

yuggib

nevertheless, he was probably born in france, or he is there since very long

Slereah

Since Indochina used to be a French colony

yuggib

@Slereah yeah I know

and he speaks a perfect french

0celo7

8:17 PM

@Slereah Proof?

yuggib

Phnom Penh

Phnom Penh (/pəˈnɔːm ˈpɛn/ or /ˈnɒm ˈpɛn/; Khmer: ភ្នំពេញ, Khmer pronunciation: [pʰnum peɲ]) is the capital and most populous city of Cambodia. Located on the banks of the Tonlé Sap and Mekong River, Phnom Penh has been the national capital since French colonization of Cambodia, and has grown to become the nation's center of economic and industrial activities, as well as the center of security, politics, cultural heritage, and diplomacy of Cambodia. Once known as the "Pearl of Asia," it was considered one of the loveliest French-built cities in Indochina in the 1920s. Phnom Penh, along with Siem...

Slereah

It's weird that he's in Lille

I looked up a lot of universities, and especially Lille since I have family there

Lille isn't big on cool physics

Oh wait, I guess he's part of the math lab, technically

Slereah

8:51 PM

Dang seems to be a pretty mathy math guy

But oh well

Close enough to my area of interest

0celo7

link

?

Slereah

math.univ-lille1.fr/~dang

Thinking about it

He got his PhD 3 years ago

I might be older than him

Not sure if he is in a position to grant thesis

John Doe

Please take a look at my question if you have some basic quantum mechanics knowldege. It doesn't look healthy because of the attachments but the questions are quite simple.

Slereah

That looks like a HOMEWORK QUESTION

TO THE STAKE!

0celo7

> Together with Laura Desideri, following a suggestion of Louis Boutet de Monvel, we seek to prove a renormalization theorem for quantum field theories on a real time analytic space by using the theory of holonomic D modules regular singularity.

@Slereah Do you understand that :P

Slereah

9:06 PM

The theory of holonomic D modules regular singularity not so much

John Doe

@Slereah It has nothing to do with homework

Slereah

BURN THE WITCH

John Doe

@Slereah I'm not at any school.

0celo7

good lord

renormalized distributions

Slereah

Well quantum fields are just distributions

So

0celo7

9:08 PM

I grabbed Milnor from the library

this thing is old

the original '65 copy

Slereah

I grabbed an original copy of Euclid's elements

All on scrolls

0celo7

proof?

ACuriousMind

-1

A: What actually happens when an anti-matter projectile collides with matter?

I just know when I'm (in tune) I take a bright light like on my cell phone...and these dark shadow imiagies get heated and also it's like I get eletricuted from these little somewhat invisible things...but, however...with the lens (camera) from a cell phone it maybe be seen...and I can even hear...

...what.

user218912

@ACuriousMind Schizophrenia?

John Doe

@ACuriousMind Is it in a sense a generalization of the approximate solution [2.75]? Is that more or less what you are saying?

Balarka Sen

9:16 PM

@ACuriousMind lol

user218912

so basically there are these invisible objects that appear when he forms a shadow by casting light on an object, and they electrocute him, furthermore if he looks that them through the lens on his camera he is able to see them and in some cases hear them and it appears as though they're taking his blood for the purpose of extracting his dna?

0celo7

@BalarkaSen You never gave me any exercises to do!

Balarka Sen

@0celo7 $X$ be a compact hypersurface in $\Bbb R^n$. Prove that it's got trivial normal bundle.

0celo7

Oh god

Is that an exercise in the book

Balarka Sen

Don't think so.

ACuriousMind

9:19 PM

@JohnDoe Griffiths is saying that at "large $\xi$" the solution is $A\exp(-\xi^2)$. So for general $\xi$, a good ansatz is $A(\xi)\exp(-\xi^2)$ such that $A(\xi)$ becomes "constant" at large $\xi$.

0celo7

Do I need Jordan-Brouwer

Balarka Sen

Nope, don't use it, because next I am going to ask you to prove J-B from this. :P

If you care, that is.

0celo7

I know that $N(Z;Y)$ is trivial iff there are global defining functions for $Z$

So I'm looking at $N(X;\Bbb R^n)$ here

Balarka Sen

Think about it. It's not quite obvious.

0celo7

is that approach wrong?

Balarka Sen

9:22 PM

Who knows? You might find a different approach.

John Doe

@ACuriousMind Okay yeah that's what I though you meant. Do you get why I am confused by the recipe he gives for terminating the sequence, since he presents it as if it is the only way to terminate and therefore leads to the energy $E_n$. Have you read some of this Griffiths book before?

Balarka Sen

I have not thought of it that way, at least.

0celo7

Can you give a hint?

Where would you put it in GP

Balarka Sen

Interesting approach tho. I wonder if I can actually see by hand that $X$ can be cut out by a global function.

@0celo7 After mod 2 intersection theory. There you go.

Note also that knowing this proves immediately that $X$ is orientable. Do you see why?

You have probably seen the relevant exercise in G&P.

0celo7

@BalarkaSen No, but I can use JB to prove $X$ is orientable.

Balarka Sen

9:26 PM

The whole point is to not use J-B :)

0celo7

You orient it as the boundary of the closure of the "interior" region.

Balarka Sen

Right.

0celo7

which inherits the orientation from $\Bbb R^n$

ACuriousMind

@JohnDoe I have not read Griffiths, and no, I don't get what confuses you about the power series.

bolbteppa

@JohnDoe If by termination you mean his reasoning for why the power series must be finite, you don't want it to, at large values, dominate over the exponential term, so it must be finite

0celo7

9:30 PM

@BalarkaSen I don't even know where to begin

Balarka Sen

Don't begin, then :)

0celo7

I don't know anything about the normal bundle of $X$

Balarka Sen

Just keep it at the back of your head. Try to picture the situation, draw idle pictures in spare time.

That's what I do when I have a hard problem to do.

@0celo7 Yes, you do: it's the bundle of normals :D

That is quite enough.

John Doe

@bolbteppa Yes I understand that. Why is that specific method of termination chosen (where all of either odd or even terms are zero), it is not the only way to terminate. But what I do note is that any method would require at some $n$ we would have $a_{n+2} = 0$, so I guess we would get the same energy $E_n$ anyway.

Maybe it doesn't matter then.

0celo7

@BalarkaSen I don't need some weird application of the TNT?

Balarka Sen

9:33 PM

Oh, yikes, I guess you need to know the statement of TNT.

But that's about it.

John Doe

@bolbteppa What do you think, does that make sense?

ACuriousMind

@JohnDoe If both odd and even terms are non-zero from the start, then their points of termination give inconsistent conditions on $K$ - if they terminate at $n_1,n_2$, you get $K = 2n_1 +1 = 2n_2 +1$, which is impossible for $n_1\neq n_2$.

The method of termination is not "chosen", it is simply not possible for a single $K$ to terminate both the even and the odd terms.

0celo7

@BalarkaSen Hmm...the normal space is 1-dimensional.

Balarka Sen

Yes, indeed.

0celo7

I'm certain the proof is in Lee :P

Balarka Sen

9:36 PM

Sigh. let me know if you need another hint tomorrow.

0celo7

@ACuriousMind what have you been up to lately

John Doe

@ACuriousMind Yes of course, that's quite true.

ACuriousMind

@0celo7 What kind of question is that?

0celo7

@ACuriousMind A normal question one human asks another???

user218912

I agree.

0celo7

9:41 PM

god, why is chat so antisocial lately

ACuriousMind

@0celo7 Sorry, I've had a not-entirely-fun weekend and haven't been up to anything I'd like to share.

0celo7

@BalarkaSen Got it.

Balarka Sen

Ah?

0celo7

@BalarkaSen $X$ is closed by Heine-Borel. Apply the theorem from analysis which states any closed set of $\Bbb R^n$ can be written as $f^{-1}(0)$ for some smooth $f$. Then apply Problem 2.3.20 in GP.

Balarka Sen

Why should $0$ be a regular value of $f$, though?

That is necessary to apply 2.3.20.

You need your hypersurface to be cut out transversely.

bolbteppa

9:50 PM

@JohnDoe Though a bit insane, you can also solve the equation more directly using Laplace "representations/method" (more accurately) if you feel this asymptotic + power series method is a bit convoluted damtp.cam.ac.uk/user/md327/fcm_6.pdf hep.caltech.edu/~fcp/math/integralEquations/…

0celo7

@BalarkaSen Hmm, I'm looking at the hint for that problem.

Why do there "obviously" exist these defining functions if the bundle is trivial?

oh, it's just the zeroes of the coordinates on $\Bbb R^k$?

Balarka Sen

@0celo7 Well, what do you mean by that?

0celo7

@BalarkaSen The coordinate functions $x^1,\dotsc, x^k$

Balarka Sen

@0celo7 Well, $X$ sits inside it's normal bundle as the zero section.

0celo7

if we set all of those to zero you get $X$