The h Bar

@0celo7 But I think it is gramatically wrong - the "piano tuners" are the subject, but "me" can't be a subject, and the case following the "than" should be the same as the thing "than" is comparing to.

0celo7

oh shut up

ACuriousMind

Mhhhh, nachos

0celo7

help me with this ODE

help with this ODE, or read page 211 ff. in BBS

FenderLesPaul

I think ODE is a politically incorrect term

check your DE privilege

ACuriousMind

I keep reading that as the German word Ode

0celo7

1:05 AM

what does that mean again

ACuriousMind

It's...a kind of song

Like a...hymn?

0celo7

or an ode?

ACuriousMind

Yeah, I think hymn captures it

0celo7

lol

you know "ode the song" is English as well

ACuriousMind

Oh

I did not know that

0celo7

1:06 AM

ode to joy

Lang wants to get all the Germans on campus together for a Stammtisch

he's really homesick, poor guy

ACuriousMind

Or he wants an excuse to import lots of German beer :D

0celo7

no, he told me he's homesick

he hates American (food) proportions

FenderLesPaul

what!

he hates freedom!

0celo7

he's scrawny like ACM

doesn't have a beard tho

also he dresses nice

ACM seems to have left

it's only 3 AM for him...he must be sick

NeuroFuzzy

1:41 AM

@DanielSank I think I figured out what was really vexing me on this.

Differential forms are usually defined/studied before the introduction of the metric

(or at least, they are in most books i've been through)

0celo7

they don't need a metric

NeuroFuzzy

but during integration of differential forms, regardless of the metric

0celo7

the metric is not needed there either

NeuroFuzzy

you're still using a lebesgue measure

0celo7

you can do everything in terms of a pullback onto R^n

you people and your analysis

NeuroFuzzy

1:43 AM

which, en.wikipedia.org/wiki/Lebesgue_measure describes as "the standard way of assigning a measure to subsets of n-dimensional Euclidean space"

and is described in the book as, "defined by pulling it back to Euclidean space"

0celo7

did I not just say that

NeuroFuzzy

("the book" meaning Renteln manifolds tensors forms pg 160)

@0celo7 :P "euclidean" usually refers to the metric too though

0celo7

the metric on Euclidean space is assumed I think

because you need a topology to define the integral on Euclidean space

NeuroFuzzy

so i was thinking, "How can I do this indepent of euclidean space, so that I have the intuition for spacetime/whatever"

0celo7

and this topology is usually taken to be that of the metric

NeuroFuzzy

1:45 AM

Yeah, you're totally right

I was trying to think of it in a way that just couldn't work :p

0celo7

you need a topology to do a partition of unity

I think

NeuroFuzzy

and more importantly you 'need' the "euclidean" lebesgue measure to do the integrals in the first place

0celo7

I dunno about that

analysis is too hard

NeuroFuzzy

Well I mean, you just use the same euclidean notion of volume/whatever

when you're looking at a parallelipiped that's just a regular euclidean thingy

0celo7

I know what you mean

so what about spacetime

FenderLesPaul

1:50 AM

are you asking how integrals are defined on a curved manifold?

NeuroFuzzy

@0celo7 oh i want to have a nice understanding of $F$ and $dF=0$ and $d \howDoYouLatexStar F=0$

0celo7

all you do for spacetime integrals is pick the volume form $\sqrt{-\operatorname{det}g}\mathrm{d}x^0\wedge\cdots\wedge \mathrm{d}x^3$

FenderLesPaul

$\star$

NeuroFuzzy

@FenderLesPaul no, i'm done asking things, I was just referring to something earlier

0celo7

\star

or *

FenderLesPaul

1:50 AM

@NeuroFuzzy ah ok

NeuroFuzzy

'cause I figured it out! Yay!

FenderLesPaul

yay!

0celo7

@NeuroFuzzy what about curvature of abelian principal bundles?

NeuroFuzzy

@0celo7 i know what six of those words mean

0celo7

@NeuroFuzzy you know that $\mathrm{U}(1)$ is an abelian group

you know that Maxwell is a $\mathrm{U}(1)$ Yang-Mills theory

you know that a $G$ Yang-Mills theory is a theory of the curvature of a $G$-bundle

ok for real this time

this ODE cannot be solved

NeuroFuzzy

1:58 AM

@0celo7 Okay... things are snapping together... I think i have to look up a better reference for a gauge theory

0celo7

@NeuroFuzzy how much differential geometry do you know

NeuroFuzzy

this book has one problem on it. "We define a gauge field theory to be a vector bundle over a smooth manifold m, where V is a vector space carrying a representation of a Lie group G"

0celo7

do you know about connections on the tangent bundle?

NeuroFuzzy

I'm just pounding through curvature and connections and christoffels and stuff, yeah

Transcript for