The h Bar

@IceLord No.

user218912

why are you asking about string theory and qm?

I don't remember doing that.

user218912

it's right ^

user218912

do you have alzheimers?

1:01 AM

hope not

I don't see what you're saying

user218912

nvm

Showing that $f\mapsto (f(p),df_p)$ is continuous on $\mathrm{Iso}(M,g)$ is hard.

This exercise is insane!

I've shown that $f\mapsto (f(p),f(p_1),\dotsc, f(p_n))$ is continuous.

user218912

ez

proof?

I'm not even sure what space that map is on.

$\mathrm{Iso}(M,g)\mapsto M\times \Gamma(TM\otimes T^*M)$ probably.

user218912

yup now i'm 100% sure I don't want to do math.

1:06 AM

@IceLord did I used to be more fun?

@IceLord Why?

user218912

yes

user218912

@0celo7 the stuff you do seems too boring in my eyes.

How is this boring?

user218912

i want to calculate stuff

user218912

and get real life answers

1:07 AM

Then why are you doing theoretical physics?

user218912

that's fun

user218912

I am doing condensed matter theory

Also I recall you once saying that you had to do really abstract physics

user218912

in condensed matter?

no, but you said that engineering was boring

applied physics was boring

I can't keep track of what's boring to you

user218912

1:09 AM

just ignore me whatever.

I thought you wanted to learn geometry and topology

user218912

yes

user218912

but in a non-rigorous way

user218912

just learn the theorems

:o

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1:10 AM

and how to use them

user218912

or even if i do proofs

that's not good

user218912

non-formal proofs only

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why?

what's a non-formal proof

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1:12 AM

like showing something is true

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without being rigorous

A proof is either a proof or incorrect.

Then it's incorrect.

user218912

only if you're a mathematician

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we physicists don't care

Aha.

$df:TM\to TM$ is continuous if $f\in \mathrm{Iso}(M,g)$.

@IceLord You're not a physicist yet.

user218912

1:14 AM

@0celo7 fine

I had that mindset when I was your age.

You'll grow up.

user218912

we're the same fucking age.

user218912

like 3 months diff.

@IceLord Mental age.

You're a Freshman

user218912

@0celo7 what mindset are you talking about specifically?

1:15 AM

@IceLord I probably would not enjoy math like I do if I didn't meet my advisor

You have a lot to experience, young one

user218912

yes I will be doing research in CMT this summer.

I...think this question isn't even hard.

I must be doing something wrong.

Where is ACM when you need him...

user218912

sleeping?

Vampires don't sleep.

@IceLord Is CMT real-life?

user218912

@0celo7 well it has applications to real life.

1:31 AM

@IceLord So what are the chances of you getting me Wolf, Lee hardcover, or Dugundji

user218912

2:01 AM

@0celo7 depends.

on?

user218912

if you can help me, but you said you don't know anything.

what is the question

user218912

it's too embarrassing to ask

ask.

user218912

2:04 AM

I still don't know how you get

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0 -1

what?

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1 0

the hell are you doing

user218912

$\begin{bmatrix}
0 & -1 \\
1 & 0\\
\end{bmatrix}$

2:06 AM

a Pauli matrix

user218912

from the rotational matrix in infinitesimal rotations

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yes

Do you know what $\mathfrak{so}(2)$ is?

First of all, do you know what $\mathfrak{so}(k)$ is in general?

I can teach you some Lie theory if you don't.

user218912

no but it's really familiar to me.

user218912

i see it everywhere.

2:09 AM

@IceLord Ok.

I will teach you the ways of the Lie.

@IceLord Do you want to know about analytic manifolds or should I skip to what you need?

user218912

@0celo7 skip to what I need, i'll learn that later.

@IceLord You won't learn it later.

No physicist besides like Geroch and other mathematical GR people know the actual theory of Lie groups.

user218912

okay then.

user218912

continue

Well, do you know how to get the Lie algebra?

How are you defining the Lie algebra

user218912

2:12 AM

idk

user218912

i didn't learn that

user218912

I should read the chapter on group theory in cahill

Then why are you asking about infinitesimal generators?

user218912

you don't need to know lie algebra for this

user218912

the prerequisites of this course are griffiths qm.

2:13 AM

Then what is your question, exactly?

@IceLord Lol, people who took that are failing my QM course

I'm not sure what you're asking bro

Do you still have Zee?

user218912

the pdf yea

user218912

ok so

user218912

how do you get $\begin{bmatrix}
0 & -1 \\
1 & 0\\
\end{bmatrix}$ from $\begin{bmatrix}
cos\theta & -sin\theta \\
sin\theta & cos\theta \\
\end{bmatrix}$

user218912

in infinitesimal rotations

derivative at $\theta=0$.

user218912

2:16 AM

oh...

user218912

that's all?

or, taylor expand in $\theta$ and take $\theta\to 0$.

user218912

what...

user218912

same thing

subtract from the identity

@IceLord not quite

but it's really the derivative at $\theta=0$

I can't give you a good explanation without some manifold theory

user218912

2:17 AM

@0celo7 you don't subtract from the identity when you're taking the derivative at $\theta = 0$ right?

user218912

nope you don't.

user218912

okay... it's that easy then

user218912

nobody told me this

user218912

TIL

well

I can explain it

user218912

2:19 AM

using what?

you want to write a finite transformation as $e^{\theta \sigma}$, where $\sigma$ is some matrix

$\theta$ is your parameter

user218912

yes I saw that form before

so take the derivative wrt. $\theta$ and $\theta=0$ you get $\sigma$

which is the thing from above

user218912

which is the infinitesimal form of the transformation?

$1+\sigma d\theta$

user218912

2:21 AM

how did you get that?

user218912

why is there a $1$

that's the definition of infinitesimal transformation...

very close to the identity

user218912

oh okay

user218912

but in my case I don't need to add the identity?

user218912

since the derivative of the identity is 0?

2:22 AM

what exactly are you looking for

$1+\sigma d\theta$ is the infinitesimal transformation

user218912

and the matrix elements themselves are?

$\sigma$ is the generator of the transformation

user218912

the derivatives ?

matrix elements of what?

user218912

where can I read more about this @0celo7

2:23 AM

Shankar

user218912

everything in the world is in shankar

It's a good book.

Very good, actually.

One of like 5 physics books worth reading, imo

user218912

okay

user218912

thanks @0celo7

user218912

<3

user218912

2:29 AM

btw 0celo7

user218912

for

user218912

$\mathcal{L} = -\frac{1}{2}(\partial_\alpha A_\beta (x))(\partial^\alpha A^\beta (x)) + \frac{1}{2}(\partial_\alpha A^\alpha (x))(\partial_\beta A^\beta (x)) + \frac{1}{2}\mu^2 A_\alpha (x) A^\alpha (x)$

user218912

to find the EOM

user218912

I just compute

I probably don't know anything about massive vector bosons.

user218912

2:32 AM

$\frac{\partial\mathcal{L}}{\partial A_\alpha(x)} = \partial_\mu \frac{\partial\mathcal{L}}{\partial(\partial_\mu A_\alpha(x))}$

user218912

right?

umm

yes

user218912

okay is that hard?

user218912

for lagrangian in question

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nvm dumb question

user218912

2:42 AM

@0celo7 I don't know how to deal with the $A^\beta$ terms in the lagrangian

user218912

what do I do with them?

lower everything with the metric

it's not a hard problem, but I would not want to do it.

user218912

oh i see

user218912

and turn them all into $A_\alpha$'s?

no, in fact

you do not want any $\alpha$s in the thing

or $\mu$s

user218912

2:44 AM

why?

no repeated indices unless they're summed

user218912

so what should I do exactly?

user218912

can you just tell me what to do and i'll try to do it

user218912

please?

post the TeX for the lagrangian

user218912

2:44 AM

I did ^

again

the code

user218912

\mathcal{L} = -\frac{1}{2}(\partial_\alpha A_\beta (x))(\partial^\alpha A^\beta (x)) + \frac{1}{2}(\partial_\alpha A^\alpha (x))(\partial_\beta A^\beta (x)) + \frac{1}{2}\mu^2 A_\alpha (x) A^\alpha (x)

thanks

user218912

the prof will probably teach us how to do this in the next 2 weeks but for now i don't know how to deal with vector field lagrangians.

user218912

so thanks

2:46 AM

$\mathcal{L} = -\frac{1}{2}\eta^{\gamma\delta}\eta^{\rho\sigma}(\partial_\gamma A_\rho (x))(\partial_\delta A_\sigma (x)) + \cdots$

then take the derivative wrt. $\partial_\mu A_\alpha$

you will get a mess

but that's the "proper" way to do it

user218912

do I do the same thing for all the other terms?

user218912

because I'm also computing $\frac{\partial\mathcal{L}}{\partial A_\alpha(x)} $

yes

user218912

so are the lagrangians the same for both derivatives?

you don't want $\partial (A_\alpha A^\alpha)/\partial A_\alpha$

that's very bad notation

so get rid of all the alphas

user218912

2:48 AM

the one wrt. to $A_\alpha$ and the one wrt. to $\partial_\mu A_\mu$ is the same lagrangian (same form)?

yes

user218912

okay

why is "thanks" starred?

user218912

idk?

user218912

@0celo7 I keep the alpha in the derivative right?

2:56 AM

yes

user218912

nvm.

user218912

@0celo7 how do I get rid of the $\mu$ now?

user218912

are you referring to the $\mu^2/2$?

user218912

doesn't that do nothing?

the index $\mu$

poor notation on your part

use $m$ for the mass.

or $M$

something like that.

3:25 AM

@IceLord do you need help

user218912

I wrote

Apr 8 '15 at 22:20, by ACuriousMind

God, you care too much about proofs. Just trust that the mathematicians are correct :D

@ACuriousMind I blame this comment.

user218912

good times.

I'm trying to figure out when I bought HE.

user218912

$\mathcal{L} = -\frac{1}{2}\eta^{\sigma\tau}\eta^{\epsilon\delta}(\partial_\sigma A_\tau (x))(\partial_\epsilon A_\delta (x)) + \frac{1}{2}\eta^{\kappa\lambda}(\partial_\kappa A_\kappa (x))(\partial_\beta A_\lambda (x)) + \frac{1}{2}m^2 \eta^{\pi\rho}A_\pi(x) A_\pi (x)$

user218912

3:30 AM

is that right?

user218912

woah

no

looks broke

speaking of

watch this

user218912

is that right now^

Channel Cheese - How to break open a Parmesan cheese with Carlo Guffanti

►

user218912

residence internet is too shit to watch videos

user218912

3:33 AM

i can barely chat

wtf

user218912

@0celo7 what errors did i make in my lagrangian?

let me look now

three kappas in one term

that's wrong

user218912

should that term be

user218912

$\frac{1}{2}\eta^{\kappa\lambda}(\partial_\kappa A_\kappa (x))(\partial_\lambda A_\lambda (x))$ ?

3:37 AM

can you not count?

now there's three lambdas too!

user218912

sorry i was thinking of something else

user218912

$\frac{1}{2}\eta^{\kappa\lambda}\eta^{xy}(\partial_\kappa A_\lambda (x))(\partial_x A_y(x)) $

user218912

yes I used latin letters

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@0celo7

wtf

I'm not reading that.

user218912

3:40 AM

how come?

ugly indices

user218912

:o

user218912

fine i'll just write the first greek letters that come to mind instead

user218912

$ \frac{1}{2}\eta^{\kappa\lambda}\eta^{\xi\gamma}(\partial_\kappa A_\lambda (x))(\partial_\xi A_\gamma (x)) $

user218912

better?

3:44 AM

what's that supposed to be?

user218912

i don't know tbh.

user218912

i tried to lower all the indices

user218912

but they were repeated so

user218912

i didn't know what to do.

user218912

that's the second term in the lagrangian @0celo7

3:56 AM

sigh

user218912

i've never done this before nor have I formally learned field theory so you can't blame me.

user218912

:(

the term is $\eta^{\mu\nu}\eta^{\rho\sigma}\partial_\mu A_\nu \partial_\rho A_\sigma$

I can blame you all I want.

user218912

isn't that what I just wrote?

oh

yes

:P

user218912

3:58 AM

good.

now tell me the derivatives

user218912

i got this

of that term

user218912

oh

I will tell you if you are right

user218912

4:00 AM

should I include the metric in the derivative?

user218912

final answer i mean

May 19 '15 at 1:05, by 0celo7

HE := Hawking & Ellis for future reference.

@ACuriousMind No. This was the moment I became a mathematician.

@IceLord no, contract everything in the end

user218912

@0celo7 okay

do you understand why you need the metrics

user218912

yes

4:02 AM

tell me.

user218912

because you can't take the derivative if the indices aren't lowered

good!

@IceLord I haven't formally learned anything

user218912

@0celo7 by formally I mean learning about it from a book or a course.

user218912

I didn't even read the notes or a book on field theory yet.

user218912

I vaguely remember it

user218912

4:07 AM

from before

before what?

user218912

last year

user218912

does the derivative become

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$\frac{\partial}{\partial A_\alpha} \bigg[ \frac{-1}{2} [\partial_\sigma A_\tau][\partial_\epsilon A_\delta]\bigg] = 0 $?

user218912

or

4:12 AM

wtf is that

oh

@KaumudiHarikumar Oh...I didn't see you there.

user228700

@0celo7 Is that supposed to be a "Hi"? :P

user218912

@0celo7 wow, don't be like that.

user218912

well it's kind of funny

user218912

xP

user228700

:?

user218912

4:14 AM

@KaumudiHarikumar did you see what he said before?

user228700

Nope. What was that?

user218912

don't worry about it.

user218912

it's not important.

user228700

Sure.

user218912

@0celo7 what is the derivative?

user218912

4:15 AM

tell me the first one please and I can infer the rest

user218912

since my index skills are bad, esp when taking derivatives.

user218912

or give a hint

0 for the A derivative

for the other one...it's harder

user218912

@0celo7 all the terms are 0?

user218912

all 3?

4:18 AM

yes

no

first two

user218912

and the last one is... let me see

user218912

brb brushing teeth

user218912

i'll figure it out in a few mins

user218912

@0celo7 the last term is $m/2$?

user218912

wait no

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4:32 AM

is it the same?

user218912

4:44 AM

can you just show me how you compute these derivatives please and i can do the rest?

user218912

@DanielSank do you know how?

5:20 AM

@IceLord What?

@DavidZ are you around?

5:42 AM

@DanielSank now I am

@DavidZ хорошо

Ha, keyboard was on Russian, so I had to.

Anyway, wanna kill ten minutes?

user228700

5:54 AM

Does anybody here listen to the soundtrack of HP while doing boring trigonometry or something like that once in awhile?

@DavidZ I'll take that as a "don't have time". I'd be interested in a real-time discussion about the homework policy and site goals at some point. Probably around ten minutes. I thought about those issues for a while today and have two thoughts that might be useful. However, before I go parading them around I'd like to have a dicussion.

@KaumudiHarikumar HP?

@KaumudiHarikumar HP = Harry Potter?

@DanielSank oh, I wasn't actively watching the chat

user228700

@JohnRennie Yes! :D

Never heard it.

5:56 AM

I've never even seen the films I'm afraid. I've read all the books though.

@DavidZ Ah. Do you have ten minutes to waste?

user228700

@DanielSank :o:o:o:o:o

user228700

@JohnRennie Oh my God.

I've neither read the books nor seen the movies.

I'm not a huge film fan. I get dragged along to the occasional film by my niece but on the whole I prefer reading.

user228700

5:57 AM

@DanielSank Wow.

@DanielSank Um... well, I can't promise my undivided attention, but that's not going to change any time in the next two weeks so we might as well do it now if you want

The last occasion being to see Mad Max Fury Road in 3D, which I have to concede was a lot of fun.

user228700

@JohnRennie OK, I see. I prefer books to movies as well, but I did watch all the movies. For a lot of kids my age, the movies are gems. I mean, we cry every time we listen to the soundtrack! It's a magical experience :-)

@DavidZ Ok. I think one of the main reasons we close homework questions is that they create buckets of questions which are implicitly duplicates of one another.

I think that is one of the two main reasons homework questions are bad.

user228700

I just figured you'd have seen HP at least.