The h Bar

Have anyone read "Quantum Field Theory and the Standard Model" by Matthew D. Schwartz? It is having a discount in the book shop, I am thinking if I should buy it, it looks promising. (personally, I have more concern on the fundamental(e.g. David Bohm) and physics (e.g.Feynman), not the math rigor .)

Danu

@ShingLau Best intro. QFT book there is

A lot better than Peskin&Schroeder

Very complete, very explicit, covers everything. Definitely recommend it

(once you get over the way he abuses index notation)

Shing Lau

12:20 AM

@Danu great, I am going to get it. Thanks.

0celo7

@Danu how does he abuse index notation

@ACuriousMind lol this emulator has AA settings

FenderLesPaul

@0celo7 he writes things like $\partial_{\mu}A_{\mu}$

ACuriousMind

@FenderLesPaul Oh god, kill that with fire

FenderLesPaul

grabs pitchfork

0celo7

@FenderLesPaul but that's wrong

@ACuriousMind $\star\mathrm{d}\star A$

does that make you feel better?

ACuriousMind

12:25 AM

@0celo7 Thanks <3

FenderLesPaul

It's still a really nice book though

I was pretty happy when I bought it

then 2 months later my ex fucking lost it

and I don't have the motivation to buy it again :p

0celo7

oh man 1.2 GB torrent

::waits::

ACuriousMind

@FenderLesPaul How do you lose a book?

0celo7

@ACuriousMind drop it into a mulcher

spill coffee on it, go to get napkins and it's gone

etc.

Danu

@0celo7 Disgustingly!

Shing Lau

12:29 AM

it is sad

0celo7

@ACuriousMind does the spacing look off to you there

ACuriousMind

Worldbuilding should be renamed to supervillain.SE

0celo7

the second star is really far from the $\mathrm{d}$

ACuriousMind

@0celo7 Yes

0celo7

@ACuriousMind you have broken me

@FenderLesPaul WW is downloading! Emu is all set up!

HDE 226868

12:30 AM

I've just encountered somebody who says that objects with masses ~ 1 M$_J$ can be classified as brown dwarfs. While his source explicitly contradicts that, and he's obviously wrong, has anybody heard anything remotely like that? (I'm guessing no).

0celo7

now I have no clue how to play a console game on a PC

HDE 226868

@ACuriousMind Yep, that's me, the supervillain of Stack Exchange.

0celo7

@HDE226868 I don't think any of us are astro people

also $M_J$

One Michael Jackson?

ACuriousMind

@0celo7 lol, what about Kyle and Chris? (Okay, they're not here right now...)

HDE 226868

@0celo7 I'm simply venting my frustration at lack of common sense. M$_J$ = mass of Jupiter. It's not a serious question.

@ACuriousMind I was afraid that people would see that question and judge.

0celo7

12:31 AM

@ACuriousMind If they were here I wouldn't have said that.

ACuriousMind

@HDE226868 I have seen. I have judged.

0celo7

@ACuriousMind Can confirm. I judged as well.

HDE 226868

in Worldbuilders' General Chat, 5 hours ago, by HDE 226868

Gotta go. 'Night, all.

Danu

Cyaaa

0celo7

@FenderLesPaul :DDDDD

@ACuriousMind :DDDDD

@Danu you probably don't care

ACuriousMind

12:38 AM

Jul 26 at 1:47, by ACuriousMind

<---never played a Zelda game

0celo7

@ACuriousMind amazing, right?

time to work out the whole controller things now

Danu

@0celo7 You're trying to bully me, aren't you? I'm the Zelda expert here!

0celo7

@Danu idk if kidding

ACuriousMind

not kidding

0celo7

lol I have no clue how to control anything

8xAA 16xAF 3xnative res

finally I can max a game out :D

@ACuriousMind i.imgur.com/FqY2JSk.jpg in honor of your Zelda prowess

ACuriousMind

12:45 AM

@0celo7 lol, I guess that's almost as good as your cat

0celo7

@ACuriousMind I did not actually do that

ACuriousMind

:(

0celo7

I'm not the fanboy from Oblivion

I always just pick "Link"

ACuriousMind

Booooring

0celo7

just like ur mum

that looks a million times better holy cow

oh wow there are mods for LoZ

ACuriousMind

12:50 AM

@0celo7 Oh no

You do have a serious modding problem

0celo7

@ACuriousMind help

haha this is maxxing out my GPU

ACuriousMind

wut

0celo7

poor optimization

oh man fans are on full jet mode

why can't I skip the cutscene...

oh this is a legendarily long opening cutscene

oh what this is like 15 fps now

@ACuriousMind this is seriously fucking up my hardware

ACuriousMind

@0celo7 Then turn off the ridiculuous AA! These games were not made to be played with AA!

0celo7

but the polygons are so pretty...

@ACuriousMind turning off AA immediately set the fps to 30

dammit

now my GPU usage is 50%

@ACuriousMind WIDESCREEN HACK

haha gamecube in 16:9

ACuriousMind

1:07 AM

Old games need to be left alone, don't mod them. :P

This is so wrong

0celo7

that's a setting in the emu

it can't change the UI unfortunately so that's stretched

so I'll change it back...

@ACuriousMind it seems any amount of AA breaks the game -- it's just not meant to run with AA

ACuriousMind

@0celo7 I told you that minutes ago :D

0celo7

shit hard crash

:( now I have to watch that cutscene again

@ACuriousMind I lowered the resolution to something that will actually fit my screen.

the emulator apparently can mod textures on the fly to make them HD

@ACuriousMind Deutschlandfaden

ACuriousMind

@0celo7 Remember the thing about basic human decency? This thread doesn't have it :P

0celo7

@ACuriousMind Ich denke du bist froh das(s) ich dir das gezeigt habe

which one is it

ACuriousMind

1:20 AM

Double s. And I really didn't need to see that.

0celo7

Ja ja, ich weis wie das ist

is weis right there

these damn ss in German

ACuriousMind

Almost, it's weiß

0celo7

ok, I couldn't type that anyway

:D

ACuriousMind

Then you should type double s instead of ß

0celo7

why can't I use the mouse for the camera D:

@ACuriousMind I know

@ACuriousMind mapping a gamecube controller to a keyboard is pretty tough

ACuriousMind

1:27 AM

Ha, I can imagine that

I don't think I've ever used an emulator for something where the controller had a stick

0celo7

there's two sticks, 7 buttons and a d-pad

I have no clue what I'll do when the game requires me to push a stick a little

ACuriousMind

You'll rage, I guess :D

0celo7

the cell-shaded graphics are great for upscaling

holy shit the mouse is an input

I can use the mouse for the camera! it works!

@ACuriousMind ah, there are ways of changing the stick sensitivity for sections where that's necessary

ACuriousMind

@0celo7 And here I was looking forward to your rage ;)

0celo7

you evil man

@ACuriousMind the math chat is talking about interacting quantum fields

ACuriousMind

1:40 AM

@0celo7 Are they saying interesting things?

0celo7

please slam them

please

they are talking about interacting quantum fields like they're well defined

ACuriousMind

Well, $\phi^4$ is well-defined in 2D and 3D...

0celo7

@ACuriousMind why is it defined in those dimensions and not in ours

ACuriousMind

@0celo7 The divergences of the integrals for the amplitude/renormalisationget worse (recall that the measure in spherical coordinates goes as $\propto r^{d-1}$.

0celo7

@ACuriousMind aha

ACuriousMind

1:45 AM

I think there's one sense in which $\phi^4$ is well-defined in 4D, and then it just gets trivial by renormalization flow, but I know no details.

0celo7

So how do you solve the fact that $\phi^4$ has a nonlinear field equation?

AFAIK distributions can't multiply.

ACuriousMind

@0celo7 Sometimes they can. But I think the rigorous construction I have in mind goes the path-integral way and doesn't talk about operators at all

0celo7

...the emu crashed again

I think this was a short-lived adventure

three hard crashes, that's worse than skyrim

I could lower the res...

@ACuriousMind Oh my you play more PoE than someone with a full-time job goes to work :P

0celo7

2:02 AM

@ACuriousMind is the path integral well-defined?

ACuriousMind

@0celo7 In these cases, yes.

0celo7

how does one know that

every term in the series converges and the series converges?

ACuriousMind

For that you should read e.g. "Quantum Physics - A Functional Integral Point of View" by Glimm/Jaffe. They first prove various convergences for stochastic integrals in Euclidean space, then present a variant of the Osterwalder-Schrader axioms, show that this well-defines the Euclidean path integral and its analytic continuation, and then spend some time checking that e.g. $\phi^4$ actually fulfills their version of the OS axioms

0celo7

I'll check that out in a few years :P

ACuriousMind

(I only skimmed that book, I have only "read" the first hundred pages where they explain stuff about QM, and I had to realize I need more functional analysis for this :D )

0celo7

2:07 AM

I wonder if I should take functional analysis

it's a year long course

ACuriousMind

@0celo7 And now I'll go to bed, exhausted from my day's "work" ;)

0celo7

cya

FenderLesPaul

I just took a nap and had a dream about Weinberg encouraging singers to follow their dreams of singing

0celo7

@FenderLesPaul so you're wide awake for some GR?

Kyle Kanos

2:34 AM

@0celo7 youtube.com/…

0celo7

@KyleKanos ack playing Skyrim

are they allowed mods at all?

that face does not look vanilla

@KyleKanos thanks btw

Kyle Kanos

No mods...it's all base game

vzn

2:53 AM

1

A: Is there any example of automatas (or similar) systems that emerge complex internal structures on its own?

as another answer states, this is a tricky question, but heres another "lead" for you that roughly fits your criteria. solitons are studied in physics and are "persistent wave patterns" that can occur in any dimension (incl physically realistic ones like 3d), based on simple energy dynamics on a ...

↑ (crosscutting/ interdisciplinary) cybersynchronicity! :D

0celo7

3:40 AM

@KyleKanos that was quick

The Dark Side

4:48 AM

@DavidZ and other mods: Not wanting to sound harsh, but I think there have been many inappropriate edits approved by a user "user36790", that I think he/she needs to be spoken to. I am sure I have seen many others like this recent one. It is almost like an edit-approve machine at work.

See edit -> approve edit -> (repeat)

Which probably explains the stats - 209 approved, 8 rejected !

(And of course, while the correction being edited into the post is right, this is not the way to do it.)

vzn

5:06 AM

in Wolfram Mathematica, 32 mins ago, by belisarius

@KyleKanos "base game"?

David Z

@TheDarkSide thanks, we'll look into it. (You can report that sort of thing via flags, too: if you want to bring attention to a member, rather than a post, flag any one of their posts with a custom flag)

Huy

7:40 AM

@vzn What's the story here? I don't know about the relation between Feynman and Wolfram at all, or what Wolfram did exactly.

Slereah

8:00 AM

mornin

It is universally accepted that Wolfram is a knob

skull patrol

8:20 AM

A very rich knob.

Would that make him a golden knob?

:-)

Made it, Ma! Top of the world!

Slereah

No amount of money can make you not a knob, I'm afraid

I knew the guy who won the Wolfram prize for proving that the 2,3 state machine was Turing complete

According to him : total knob

skull patrol

It can buy you a lot of knobby "friends."

Slereah

Also he is a bit of a crank I hear

skull patrol

Or should that be snobby friends?

Slereah

His book on "Doing all of physics with cellular automaton" was not received well

skull patrol

8:28 AM

Oops, another tax write-off.

@Huy do you know what happened between Chris's sis and Khallil?

When I got there, there were 8 mods in the room and one of them thought I was her and threatened to suspend me :(

Huy

@skullpatrol: I saw that Chris'ssis posted a picture of an introduction of a book (not written by him/herself) on integrals. The introduction itself seemed rather condescending, similar to how Chris'ssis talks to people who don't like his/her obsession with integrals in chat.

@skullpatrol: Several people pointed out that such an introduction is rather condescending (and also what exactly about the introduction) and Chris'ssis stated that the author had no reason at all to be condescending, since the book was all about integrals.

@skullpatrol: After some discussion, if I recall correctly (not sure about the exact wording!), Chris'ssis started saying things to Khallil in the spirit of "write a better book, you don't know anything about integrals to begin with, so who are you to state your opinion, your opinion is worth less because you know nothing about integrals whereas I do", and after I was AFK for a few minutes, Chris'ssis was suspended and lots of messages were deleted.

skull patrol

8:43 AM

Tsk, tsk...the drama never stops :P

Huy

@skullpatrol: chat.stackexchange.com/transcript/message/23240921#23240921 This is where it begins.

skull patrol

Thanks for the info pal @Huy

skull patrol

10:07 AM

OMG they froze the entire math room :O

Huy

@skullpatrol: Great!

Danu

11:12 AM

Nice, CFT by Blumenhagen & String theory 1 by Lüst! The masters themselves :D

ACuriousMind

::barely contains envy::

Slereah

Hello

ACuriousMind

@Danu My QFT lecturer was a PhD student of Lüst and Blumenhagen, actually

skull patrol

Has this room ever been frozen @ACuriousMind?

ACuriousMind

...that sounds as if he'd still been a student when he lectured. Is there a better way to express it?

@skullpatrol lol, yes, very recently in fact

skull patrol

11:22 AM

:(

ACuriousMind

I have mentioned that I hate HNQs, yes? That conversation law answer is now my third-highest voted of all time -.-

Slereah

"if you drop an electron, its spin changes. If it didn't, it wouldn't fall down."

Damn you Duffield

ACuriousMind

It's really a shame one can't downvote comments :P

Slereah

you can flag them

ACuriousMind

Yeah, but being wrong is not a reason for deletion for answers, why should it be for comments?

I'd answer that question if I knew exactly how to work with spinors in curved space, but the answer looks to me to be that a spinor field is a spinor field independent of coordinate choice.

Danu

11:37 AM

@ACuriousMind conversation law :D

ACuriousMind

@Danu oh xD

Slereah

I would answer but it would involve me doing calculations

Danu

@ACuriousMind LMU best U

Slereah

Like I'd have to apply coordinate change to the spin tensor

Then integrate it

and that's not what I'm about

ACuriousMind

11:48 AM

Honestly, does this question make actual sense to anyone?

Danu

Lol, so the math chat rage spread to english language? lmao

Huy

@Danu: Math people.......

Danu

@ACuriousMind Not really

ACuriousMind

I hate bounties on non-sensical stuff

I think the only reason I didn't vote to close when I made my first comment was that I hoped that OP had an actual well-formed question, and then I just forgot about it.

Slereah

but then you can answer nonsense and collect the bounty

ACuriousMind

11:52 AM

@Slereah Yep, that's how you earn bounties ;)

Slereah

Hey, for once that I get points for a long answer :p

Usually I get them for two lines answers

And the giant ones are ignored!

ACuriousMind

@Slereah Tell me about it, I suffer from the same

Danu

You jelly, broski's?

ACuriousMind

@Danu That's not even worth a gold badge :P

Danu

@ACuriousMind You're not even worth a gold badge!

ACuriousMind

11:59 AM

I am.

Danu

Didn't even have to click that.

ACuriousMind

Well, I only have the one :D

Danu

Disgusting quantum sellouts

Slereah

The secret to success is to answer soft questions

"What color was Schroedinger's cat""

Huy

@Danu: Be honest, Tdonut is another account of yours and you just wanted to write such a summary as soon as you finished studying GR.

Danu

12:02 PM

@Huy Lolololol.

In fact, I already learned GR about 2 years ago :P

ACuriousMind

@Slereah We know.

HDE 226868

@ACuriousMind Referring to your comment a while back: Not really. And, of course, John Duffield answered it.

Huy

@Danu: So it took you two years to write that post, and then you had to wait an hour before answering because otherwise it would have been too suspicious, at the same time hoping nobody else would post a great answer before you!

ACuriousMind

@Huy is on to you, @Danu!

Danu

:'(

I think it's time to hand in my moderator badge for sockpuppetry :P

Also, rate on a scale from 1 to 10 how terrible I am for skipping Galois theory?

ACuriousMind

12:06 PM

@Danu $\pi$

Danu

@ACuriousMind That's about how I feel (also we're not counting down like the Germans, right?)

It just seems so utterly irrelevant for physics :P

I think I'd enjoy it if I got some lectures on it. But that's not the case :\

ACuriousMind

Yeah, Galois theory is the thing I really don't know a physical application for

Dominic Michaelis

Hello

skull patrol

Hi pal

Danu

On to representations and Lie groups ^^

Dominic Michaelis

12:07 PM

how the hell does a physician define operator?

0celo7

@Slereah what

Danu

PHYSICIAN?!

Grrrrrr

ACuriousMind

lol

Danu

physicians work with people

Slereah

@0celo7 I don't knooow

Danu

12:08 PM

physicists do useful stuff

@DominicMichaelis Totally depends on the context.

Dominic Michaelis

@danu oh sorry english is foreign language

ACuriousMind

Do you mean a quantum mechanical operator?

Danu

@DominicMichaelis No problemo (I was just kidding): en.wikipedia.org/wiki/Physician

Dominic Michaelis

yes

0celo7

@Danu that's a common mistake by native speakers as well

Huy

12:09 PM

@Danu: But Galois theory is the coolest thing you're gonna learn from algebra, probably.

Danu

@ACuriousMind Please don't answer it in your style

ACuriousMind

That's just a linear map from the space of states to itself, then.

Danu

@Huy It seems really boring in this book :\ Fields are like... mehhhhh

Slereah

There's a mathematician band

Huy

@Danu: :(

Slereah

12:09 PM

They made a western song about Evariste Galois

Huy

But.. Abel-Ruffini :(

Danu

@Huy Can you give any application to geometry? or physics?

Dominic Michaelis

@ACuriousMind that is exactly what I thought, but the momentum operator doesn't map into the same space

ACuriousMind

@DominicMichaelis Oh, I think you've found one of the subtleties, then! Tell me why it doesn't map into the same space

Slereah

An operator is just a linear map from the Hilbert space to itslef, no?

ACuriousMind

12:11 PM

@Slereah There are subtleties in the infinite-dimensional case. I want to see if this is about one of them, or about another misunderstanding

Slereah

It's basically just a rank 1,1 tensor :p

Dominic Michaelis

@ACuriousMind well a wave is a function from which maps from $\mathbb{C^3} \times \mathbb{R}$ to $\mathbb{C}$

ACuriousMind

Why does it start at $\mathbb{C}^3$?

And the $\mathbb{R}$ is the time?

0celo7

@Huy abel was weak

Dominic Michaelis

@ACuriousMind well because the momentum operator shall be $- i \hbar $

times nabla, yes $\mathbb{R}$ is the time

Huy

12:13 PM

@Danu: I'd guess you can use it to understand groups better, the fundamental group mostly in physics, but I don't know. I didn't need an application because I was eager to understand the proof of Abel-Ruffini.

Dominic Michaelis

if you like we can start from $\mathbb{R}^3 \times \mathbb{R}$

Huy

@Danu: Also I'm not at all in that field, in fact algebra is probably my weakest part of maths education.

ACuriousMind

@DominicMichaelis Yep, a wavefunction is thought to be a square-integrable function on $\mathbb{R}^3$.

Dominic Michaelis

doesn't make a difference, but the momentum Operator is $- i \hbar \nabla$

Huy

@Danu: Maybe BalarkaSen from MSE can give you precise examples, if you really want to know.

Dominic Michaelis

12:14 PM

so $ \nabla \psi$ will map to $\mathbb{C}^3$ and not into $\mathbb{C}$

ACuriousMind

@DominicMichaelis Ah, I see. Well, in more than one dimension, you don't have "the" momentum operator. You have the three operators $p_x,p_y,p_z$, which are the partial derivatives in the respective directions.

And, sometimes, one writes them into one "vector of operators" $p = \nabla$, but they're really three operators.

Something about such "vectors" is asked and answered here

Dominic Michaelis

@ACuriousMind oh i see, kind like that makes it very hard for me to unterstand what is standing in the lecture notes

ACuriousMind

@DominicMichaelis I recall also being confused at this point, most texts/lectures suck at making it clear what such a "vector of operators" is meant to be.

Dominic Michaelis

@ACuriousMind yeah and I got the feeling my prof doesn't know what he is doing, he wrote the hamilton operator as a $2\times 2$ matrix ...

0celo7

@DominicMichaelis "standing" you must be German!

Dominic Michaelis

12:18 PM

@0celo7 oh yes I am

ACuriousMind

@DominicMichaelis Well, there are instances where the Hamiltonian is a 2x2 matrix (e.g. in a two dimensional system :P), or when it acts on things with half-integer spin

Dominic Michaelis

@ACuriousMind because he suggests to solve $\det(A- \lambda id)=0$ to find eigenvalues of operators

ACuriousMind

@0celo7 lol, didn't even notice that wasn't English

0celo7

@ACuriousMind steht

ACuriousMind

@0celo7 Yeah, I just translated it as that and didn't notice anyting odd

@DominicMichaelis Well, solving the characteristic polynomial for its roots like that is how you'll do it in most finite-dimensional cases

Dominic Michaelis

12:21 PM

but even though I am very familar to functional analysis I got no idea how someone wants to define a determinant for operators (let them be self adjoint between hilbert spaces)

0celo7

@ACuriousMind you think in German when chatting in English?

ACuriousMind

@DominicMichaelis The physicists in introductory QM (and beyond that) like to pretend everything is linear algebra :P

And in the exercises, I guarantee you'll only be asked to do things where that goes through (e.g. you'll only be asked to determine eigenvalues on finite-dimensional spaces)

The whole functional analysis is sadly swept under the rug by most

@0celo7 ...not sure. When I try to listen to my thoughts it's kinda...mixed

Dominic Michaelis

But I thought we act on $L^2(X)$ for $X$, so I am pretty confused. After all we say that the spectrum only has eigenvalues, and they are always diagonalizable, but this is even wrong with $2 \times 2$ matrices

0celo7

@ACuriousMind I think in a British accent

makes me sound smarter to myself

Dominic Michaelis

In fact I mean noncommuting products, which aren't self adjoint (even though the factors are self adjoint)

Huy

12:24 PM

Fredholm determinant

In mathematics, the Fredholm determinant is a complex-valued function which generalizes the determinant of a matrix. It is defined for bounded operators on a Hilbert space which differ from the identity operator by a trace-class operator. The function is named after the mathematician Erik Ivar Fredholm. Fredholm determinants have had many applications in mathematical physics, the most celebrated example being Gábor Szegő's limit formula, proved in response to a question raised by Lars Onsager and C. N. Yang on the spontaneous magnetization of the Ising model. == Definition == Let H be a Hilbert...

0celo7

@ACuriousMind do you have a cat dictionary? I have one squeaking at me for something

ACuriousMind

@DominicMichaelis Yeah, if you have a position operator, you're on $L^2(\mathbb{R}^n)$. But you don't always have a position operator. E.g. there are instructive cases of $n$ particles with half-integer spin who can't move, and their space of states is not $L^2(\text{anything})$, but just $\mathbb{C}^{2n}$.

@Huy Yeah, that one fails totally because position and momentum are usually not trace-class or bounded :D

Huy

@ACuriousmind: I just wanted to bring an example of how to define a determinant for operators.

ACuriousMind

@0celo7 You have a dictionary squeaking at you? oO

0celo7

@ACuriousMind yes, help

ACuriousMind

12:28 PM

Tell it new words, perhaps that'll satiate it

0celo7

he was just hungry

no clue why someone else didn't feed him

Dominic Michaelis

@ACuriousMind I would really like to have a reference where Quantum Mechanics is treated mathematically, so telling something like how the domain of the operator really looks like

ACuriousMind

@DominicMichaelis I like this paper. It's not a self-contained introduction, but it addresses many of the subtleties that occur typically in introductory QM

It's a nice addition to a typical QM course, I think.

Dominic Michaelis

I really would like to see that vector space of eigenfunctions ...

ACuriousMind

@DominicMichaelis Ah, that's not even a Hilbert space! Look at rigged Hilbert space/Gel'fand triples for that (we also have some questions here on the site)

The paper I linked also discusses that, I think (look for where they talk about Schwartz functions)

@DavidZ "engineering", really?

I mean, it's off-topic, but that's not an engineering question.

Dominic Michaelis

12:40 PM

I really like the argument, that the solution must be $C \exp(x)$ but because this is not bounded which doesn't make sense in physics $C$ must be zero ...