The h Bar

1:11 AM

@Danu so if we do some scalar field wankery in ads, we can compute propagators, some kind of boundary to bulk or boundary to boundary. So is boundary to boundary the same thing as cft 2-point corr function? Is this some corr function realization of ads/cft? the other being something with partition functs

So then one can do some ops with X_i's and find corrs(insertions) to get things like ward id's. How does one match the ads side?

@Danu I have an idea, about some ads/cft stuff. Can I run it by you in full sometime. I want to run it by people who know this stuff before I bother pursuing it :^)

0celo7

3:06 AM

@ACuriousMind I can't read cursive or German

Ok I can read German but not cursive German

@ACuriousMind ...really?

That much work?

@ACuriousMind Why no bar on your z

"stetig"

Is that...

monotone?

Oh, maybe continuous

Ok, I think I understand your proof

Dunno why you handwrote that, you're not in 14th century feudal Germany

user116211

4:03 AM

@0celo7 Is this ACM's writings?

0celo7

yes

user116211

@Danu Germany is still alive ;))

user116211

And I would be surprised if they win against France.

user116211

I like that they still believe in 4-4-2 formation. This has become quite outdated and rare recently.

user218912

4:52 AM

@MAFIA36790 you mean iceland

user116211

6:01 AM

@3750 yes.

ACuriousMind

9:50 AM

@0celo7 Uh, I still handwrite faster than I TeX?

@0celo7 Better to be safe - I would have written "obvious" but I suspect I wouldn't have gotten the points for that :P

Slereah

10:34 AM

@ACuriousMind maybe it's because this chat is nothing but math

MonaLisaOverdrive

10:45 AM

'lo

Slereah

Hello

MonaLisaOverdrive

Got a somewhat meta physics question…a 'making sure I'm studying the right stuff' question

Ok to ask here?

Slereah

Sure

MonaLisaOverdrive

Great, thanks!

I'm on a tablet so bear w/me

Currently reading Susskind's The Theoretical Minimum: QM in parallel with Linear Algebra for Dummies. Are these appropriate materials if I'm interested in probability in QM?

Keep in mind I am a curious layperson, not a physicist or a mathematician, so…

Slereah

Not a clue

Never read it

MonaLisaOverdrive

10:58 AM

Ok, fair enough. Any books/articles you'd recommend on the subject?

Susskind's book is…it walks through the basics of QM including the mathematics. Think QM for the Idiot Physicist

Okay, one last question before I hit the books: Is it possible to have a non-rectangular matrix? Or is a matrix by its very definition, rectangular?

Balarka Sen

What do you mean by "non-rectangular"

MonaLisaOverdrive

Something like this:

x x1 x2 x3 x4
x x1 x2 x3
x x1 x2

Balarka Sen

What use would it be of?

You can just put 0's below the diagonal and make it into a matrix anyway

MonaLisaOverdrive

ah

Balarka Sen

(also, yes, matrix is by definition "rectangular")

I mean, defining something has to have a purpose. What's the purpose of defining an array of numbers arranged in a, I dunno, pentagon?

MonaLisaOverdrive

11:13 AM

I don't know, honestly. It was a question that came to mind when reading about matricies

Balarka Sen

It will probably not be very useful.

MonaLisaOverdrive

Ah

Are there three-dimensional mathematical objects…i.e. numbers arranged in a cube?

Or sphere?

Balarka Sen

@MonaLisaOverdrive Yes. Those are useful.

MonaLisaOverdrive

Interesting

Balarka Sen

keyword is "tensors".

MonaLisaOverdrive

11:16 AM

very interesting.

But no spherical, circular or other shapes of mathematical objects?

Balarka Sen

None that I know of which is used terribly frequently to do genuinely interesting things in mathematics.

MonaLisaOverdrive

Ah. Thanks. And thanks, all, for patiently answering my questions. Back to studying

Note to Self: mathematics are straight, as opposed to curvy

Balarka Sen

Not really. But you're doing linear algebra after all.

Naively speaking, in that part of mathematics, it doesn't help to start with objects which are "nonlinear", whatever that might mean.

In any case, the shape of the matrix doesn't really matter. What matters is how two matrices interact.

MonaLisaOverdrive

Ah. Thanks for the correction. Is there a specific branch of mathematics that covers 'curvy'?

Is it calculus?

Balarka Sen

You can say that.

MonaLisaOverdrive

11:28 AM

Ok. Now, really, back to understanding how a linear operator represents an observable

MonaLisaOverdrive

12:30 PM

I

user685252

12:56 PM

O

John Rennie

1:55 PM

@MonaLisaOverdrive Susskind's book is pretty good. In fact it would be a sound base to start from if you decided to take physics more seriously.

user252685

Susskind has some great work on youtube

0celo7

@JohnRennie Hmm, why not learn some math first?

Understanding Analysis by Abbott is very good.

@JohnRennie Then read Lee's set of three books, then Wald.

user252685

2:13 PM

now look what you did

user116211

@0celo7: Any plan for July 4 holiday?

0celo7

@MAFIA36790 driving home from brother's house

user116211

oh.

user252685

have you named your car yet?

0celo7

@user252685 "Old Woman Killer"

user252685

2:27 PM

:(

MonaLisaOverdrive

@user252685 That "I" was from trying to type in chat from a tablet

user252685

iPad?

MonaLisaOverdrive

Android

Multiple tabs, chat froze

Thanks for the suggestions @JohnRennie and @Ocelo7

user252685

how much math do you know?

that^ is the rate determining factor

MonaLisaOverdrive

Not much. Just started reading Linear Algebra for Dummies. Other than that, just high school level calculus, algebra, etc

Reading that in parallel with Susskind

Read some maths books a few years ago, but basic stuff: set theory, proofs. Minimal practice exercises

Balarka Sen

2:34 PM

Linear algebra is good stuff.

MonaLisaOverdrive

It's been interesting so far.

Wish I'd had the Dummies books in high school math

Balarka Sen

It's a good place to start learning math, IMO. Set theory, analysis etc are more fundamental, but may seem somewhat dry for a beginner.

Physics Meta

0

Q: Why Was This Elementary Question Closed?

I do not understand why this elementary question was closed. The official reason calls it a "homework-like question" and asks the poster to "show some effort". One could argue about whether this is homework-like (though it seems clear to me that this is not an assigned problem, but rather som...

discussion

MonaLisaOverdrive

The set theory was part of the proofs book I was reading. Not sure what analysis is

Balarka Sen

Where did you read it from? (analysis is calculus with steroids)

MonaLisaOverdrive

2:39 PM

Read what from?

Balarka Sen

Set theory, I mean.

MonaLisaOverdrive

Ah. How to Prove It by Velleman

Balarka Sen

I see.

user252685

there are no uses for steroids in math :P

MonaLisaOverdrive

Was reading it for Fermat's Theorem

Calculus w/o steriods is challenging enough

So…calculus is a subtopic of analysis, according to the internet

Balarka Sen

2:48 PM

Yes.

MonaLisaOverdrive

…or not. Appears as though there's some vigorous arguments about it on StackExchange. EDIT: nm, just saw your reply @BalarkaSen

Taking off for a bit…work and such

user252685

later

0celo7

@BalarkaSen @ACuriousMind A connection is metric iff parallel transport is an isometry of the corresponding fiber metric.

Balarka Sen

3:03 PM

@0celo7 Cute.

By metric, you mean compatible with the Riemannian metric, yes?

0celo7

@BalarkaSen yes

Torsion free is still a mystery

user116211

3:21 PM

@yuggib: Got Jech's Set Theory.

user116211

What a book, dude; it explains the axioms' necessity first with a brief note on Russell's Paradox....

user116211

At the first look, the writing seems to be lucid and clear...

user116211

reading

user116211

Good, @Balarka is now regular here ;)

Balarka Sen

only temporarily, i assure you

0celo7

3:36 PM

@BalarkaSen why only temporarily

Balarka Sen

physics is too hard for me

Physics Meta

0

Q: How to suggest edits for help center pages

This question identified a grammatically incorrect phrase in the What does it mean when an answer is "accepted"? help center page. (Note: This particular page appears to be used across the stackexchange network. The problem is endemic.) From what I can see, there's no edit button that lets one p...

discussion support

user252685

@BalarkaSen are you feeling any better?

Balarka Sen

4:03 PM

much better, yes

user252685

@BalarkaSen good to hear :)

vzn

@MonaLisaOverdrive gibson fan?

@Balarka are you in college yet?

MonaLisaOverdrive

4:23 PM

@vzn Of course.

vzn

4:44 PM

@MonaLisaOverdrive have you read any of his books? what country are you in? are you in highschool?

yuggib

@MAFIA36790 yeah, it's a neat book

and cardinals/ordinals are very nice

0celo7

@BalarkaSen you around?

yep

5:01 PM

@vzn Yes, NA, nope.

6:40 PM

Dumb question. Where the hell does the thing of writing "+ve" and "-ve" instead of "positive" "negative" come from?

kevin Tah N.

7:57 PM

@Danu please come visit me sometime chat.stackexchange.com/rooms/41774/…

@3750 hey dude

0celo7

8:33 PM

@ACuriousMind I'm really starting to like the notation $M_p$ as the notation for $T_pM$.

It's consistent with the notation $P_x$ as the fiber of the principal bundle $P(M,G)$ over $x\in M$.

I think.

user218912

9:37 PM

@0celo7 you around?

user218912

@kevinTahN. hi

Pichi Wuana

9:52 PM

Hi

0celo7

10:06 PM

@3750 barely

user218912

10:17 PM

@0celo7 don't laugh at me but carroll exercise 1.11, idk how to do it.

user218912

well my main issue is deriving $$\partial_{[\mu}F_{\nu\lambda ]} = 0$$ from maxwell's equations.

user218912

it's the third maxwell equation idk how to denote using the field tensor.

0celo7

hmm, that is a Maxwell equation...

user218912

yeah.

user218912

how do you get it from equations 3 and 4?

0celo7

10:28 PM

3 and 4?

check Chap 4.3, maybe 4.2 of Zee

he does it

user218912

he does it differently.

user218912

I need to use the same line of reasoning as carroll.

0celo7

beats me what his reasoning is

user218912

like by saying $F^{0i} = E^i$ and $F^{ij} = \epsilon^{ijk}B_k$.

0celo7

just plug in different values for $\mu,\nu,\lambda$ and check that you get traditional maxwell equations

user218912

10:31 PM

how does $\epsilon^{ijk}E_k$ relate to the field tensor?

0celo7

dunno

user218912

cmon...

user218912

if you have $\epsilon^{ijk}\partial_j E_k + \partial_0 B^i = 0$

user218912

that's the third maxwell equation

user218912

how do you express it using the field tensor.

user218912

10:33 PM

do you know?

0celo7

just see what like $\partial_{[\mu} F_{0i]}$ is

fuck

user218912

oh right

user218912

also how come the indices of $F$ are now at the bottom?

0celo7

well you have to raise them

actually I don't know how we defines $F_{\mu\nu}$

I'm not a physicist

I do not actually know what $A_\mu$ is

user218912

would it make sense to write $\partial_{[\mu}F^{\nu\lambda ]} = 0$

0celo7

10:36 PM

probably not

user218912

$A_\mu$ is just a vector potential?

0celo7

the equation is really one in terms of diff forms written for n00bs

user218912

yeah I remember learning that.

user218912

so is $\epsilon^{ijk}\partial_j E_k = \partial_{[j}F_{0i]}$

user218912

?

user218912

10:46 PM

no that's wrong.

NeuroFuzzy

@3750 Correct!

user218912

it's equal to $\partial_jF_{0i}$?

user218912

right?

user218912

@NeuroFuzzy can you help me do this derivation?

NeuroFuzzy

Hmm...

(reading)

Oh, wow, so, "maxwell's equations" as in the vector form?

user218912

10:50 PM

yeah.

user218912

how do you express $B^i$ using the field tensor?

user218912

does $\epilson^{ijk}\partial_j E_k + \partial_0 B^i = \partial_j F_{0i} + \epsilon^{ijk}\partial_0 F^{jk}$?

user218912

does $\epilson^{ijk}\partial_j E_k + \partial_0 B^i = \partial_j F_{0i} + \epsilon^{ijk}\partial_0 F^{jk}$?

NeuroFuzzy

@3750 So, one nice way to think about things to answer questions like these

is write $F^{jk}$ as a matrix {{0,-bz,by},{bz,0,-bx},{-by,bx,0}} (Plus or minus this, I forget)

then $\varepsilon^{1jk}$ is the matrix {{0,0,0},{0,0,1},{0,-1,0}}. Comparing the two matrices (not using matrix multiplication, just as placeholders), you find $\varepsilon^{1jk}F^{jk}=-2B_x$.

(Summation convention. If I got the sign of $F^{jk}$ right.)

@3750 so yep, it looks like you're on the right track.

user218912

11:18 PM

sorry my wifi broke.

NeuroFuzzy

NP. I'm being slow on this because it's an annoying problem anyways haha

Also: I would stick with $F^{jk}$ and just use repeated index = summation

user218912

though for the $\epsilon^{ijk}$ shouldn't the indices be down on the right side?

Slereah

What is an epilson

user218912

dude

user218912

I made a typo and lagged out.

user218912

11:20 PM

couldn't fix it :(

NeuroFuzzy

@3750 I call them "summation convention" and "einstein convention"

user218912

I think it should be $\epsilon^{ijk}\partial_j E_k + \partial_0 B^i = \partial_j F_{0i} + \frac{1}{2}\epsilon_{ijk}\partial_0 F^{jk}$?

NeuroFuzzy

@3750 oh, I know! Did I say something that sounded rude? It's an annoying problem 'cause you have to break apart and reassemble everything.

I think there's a factor of $\frac{1}{2}$ in there

user218912

yeah but carroll omits it.

user218912

I think.

user218912

11:22 PM

right it should be

user218912

edited^

user218912

and the final equation is

user218912

$-\frac{1}{2}\epsilon_{ijk}\partial_i F^{jk} = 0$?

user218912

no

user218912

should the index in the partial be on top?

NeuroFuzzy

11:31 PM

@3750 My opinion is to stick with one choice and use the repeated index convention

user218912

so how should it be?

NeuroFuzzy

It's a choice. The symbol $\varepsilon_{ijk}$ isn't a tensor, I don't believe, so when you get equations with it it's hard to be consistent.

I would probably write it like you had written it, and somewhere on the page I'd write "(repeated index convention)" to make it clear

but yeah, when you pull a tensor apart into components it's hard to impossible to stay consistent with the indices.

and you don't want to be confused between $F^{jk}$ and $F_{jk}$, etc.,

user218912

oh

user218912

one is the dual of the other?

NeuroFuzzy

Sort of. Dual isn't really the right word. For example, if you use the convention with the metric $ds^2=dt^2-dx^2-dy^2-dz^2$, then $F_{22}=-F^{22}$

oh wait that's not right

lol

$F_{22}=-F_2^{\ 2}$

with that metric convention

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