The h Bar

DIRAC1930

1:04 AM

It depends how projects are selected by the funding organizations. When writing grant applications, there are question boxes that now ask for technological applications and time frame etc which essentially puts a complete end to research in more fundamental areas.

I get this for hep-th (which is why most of funding comes from the department for those projects), but it's gotten to a point where even standard areas of condensed matter theory are being heavily targeted.

Honestly, I kind've feel bad for a lot of the condensed matter theory profs. There used to be several in my old departments…

Silly Goose

not me misreading a table of definitions for coefficients and performing 20+ integrals using my incorrect misreadings...

Obliv

it happens to the best of us

Silly Goose

@DIRAC1930 one program i visited i was excited about, but then when i talked to the CMT people in the department, they either had $0$ funding or were planning to take a single student. sadge.

lucabtz

2:55 AM

@ACuriousMind this is the kind things I've been asking about on this chat for a while

Silly Goose

5:37 AM

who started this bundle theoretic approach to field theory? or what are some of its origins

Sir Cumference

6:06 AM

why are papers so expensive to read

like most journals charge around $40 per paper

naturallyInconsistent

6:19 AM

@SirCumference isnt this highly criticised?

Silly Goose

@SirCumference there is a hub of science similar to the genesis of libraries

naturallyInconsistent

lol

Slereah

6:40 AM

@SillyGoose Cartan I think?

Silly Goose

dang that's a long time ago

well okay i guess not that long ago

Slereah

I mean bundles themselves are at most from the 30's, if you go really far back

I think it got into physics in like the 50's, but as a pretty marginal use

You don't really see bundles that much until the 60's I think

During the whole GR renaissance

Silly Goose

i see

Slereah

Probably inspired by the use of bundles in famous differential geometry books like Kobayashi

Silly Goose

oh mayn that's the K in CKM

Slereah

6:45 AM

CKM?

Silly Goose

oh maybe not the same kobayashi

ckm matrix related to standard model

Slereah

Oh yeah no, Kobayashi is a super common name in Japan

Silly Goose

ohh i see

Slereah

It's like Smith

You may also remember it from Star Trek

The Kobayashi Maru test

Silly Goose

i never watched star trek but many physics students and professors seem to have

Slereah

6:49 AM

I have been looking into like the trends in styles of differential geometry through history

The sleek modern method is mostly due to Kobayashi et al

Sir Cumference

@naturallyInconsistent I mean paying to read research as a whole is highly criticized

but the price alone just boggles my mind

if arxiv (or "other means") didn't exist you could spend hundreds of dollars a month just to keep up with the latest research

Slereah

I think people in the olden days just borrowed them from the library :p

naturallyInconsistent

7:07 AM

@SirCumference monopolies do the shit that they do

Sir Cumference

that is true sadly

paying $40 so i can read a 4 page paper sounds like a ripoff, except that there isn't an alternative

naturallyInconsistent

capitalism gotta ruin everything

@SirCumference technically, this is totally false. We can easily implement a different system and not be beholden to the status quo

Sir Cumference

@naturallyInconsistent so what's the hold up

i mean academia has a weird system where we value prestige over money

i feel like switching that trend would probably be difficult at this point

123

Hello Everyone...

Slereah

I mean by now I think most people in physics will just read the preprint :p

Sir Cumference

7:15 AM

@Slereah well thank god that's an option lol

Silly Goose

i don't really understand something. we set up classical chern-simons theory and then find "gauge" transformations that do not leave the classical action invariant, but will turn into gauge transformations post-quantization of the theory?

Sir Cumference

i'm surprised journals haven't tried to lobby for that being a copyright violation or something

Silly Goose

so is classical chern-simons theory not really anything but a set up for a quantum theory?

Slereah

@SirCumference How can it be, this is published before the journal

Sir Cumference

@Slereah well that's true

i guess they can't do much about it even though it takes away almost all their income

Slereah

7:18 AM

They don't really make their money on individual sales of articles

They mostly sell subscriptions to universities

naturallyInconsistent

@SirCumference what part of "nobility culture" is weird to the hooman condition? Hoomans have had monarchy for millennia.

Silly Goose

i guess per this post it seems the point of singling out large gauge transformations is to have in mind the quantized state space

More Anonymous

7:36 AM

Here's something I was wondering about... Does evolution prefer almost parity symmetric organisms? How would one go about showing this is the case?

qwerty

@SirCumference usually libraries would buy them, and you'd just ask for your local university library membership

More Anonymous

Like if I asked what is the probability of an assymetric organism surely there would be a non zero number?

qwerty

@SirCumference they dont need to, academics will publish in journals regardless of preprints

Silly Goose

blebs but ACM's answer says that classically large transformations are still genuine gauge transformations. but in the classical chern-simons theory it seems like they are not because they genuinely change the action

Slereah

8:00 AM

Well then it's not a symmetry of the action :p

Silly Goose

8:12 AM

hm is being a symmetry of the action not a necessary condition for being a gauge transformation?

qwerty

8:59 AM

"The combination of push forward and coordinate transformation is an example of a diffeomorphism. A diffeomorphism is a one-to-one mapping between the manifold and itself. ... In a diffeomorphism, we shift the point at which a tensor is evaluated by pushing it forward using a vector field and then we transform (pull back) the coordinates so that the shifted point has the same coordinate labels as the old point."

Is there another name for the specific operation of "shifting the point on the manifold combined with changing coordinates"?

12

A: In general relativity, are two pseudo-Riemannian manifolds physically equivalent if they are isometric, or just diffeomorphic?

Indeed, "diffeomorphism invariance" of GR in physics in this context means in proper mathematical parlance that isometric (pseudo-)Riemannian manifolds are physically equivalent. In my view, this confusion between "diffeomorphism" and "isometry" is probably due to physicists usually looking at a ...

"define the diffeomorphism to be an isometry so that the fields on the target with the new coordinates are equivalent to the fields on the source."

is it an "isometry"?

Slereah

An isometry is just a diffeomorphism that preserves the metric

qwerty

because the coordinates of the new points are the same as the coordinates of the old points, then the distance between two new points must be the same as the distance between the two old points under this operation, right?

and the pushforward by itself is also an example of a diffeomorphism, but not an isometry?

Slereah

9:17 AM

Isomorphisms fundamentally preserve norms, but it is also true that it preserves distances, yes

Flow of a curve by an isometry leads to a curve of the same length

Ryder Rude

hi

Ryder Rude

9:37 AM

would u say u r more mathematical than most physicists or less mathematical

qwerty

wait. pushfowards act on vectors, not points according to baez? bertschinger's notes are confusing.

Slereah

Yes

Diffeomorphisms act on points

Their pushforward on vectors

qwerty

this quote "The combination of push forward and coordinate transformation is an example of a diffeomorphism. A diffeomorphism is a one-to-one mapping between the manifold and itself. ... In a diffeomorphism, we shift the point at which a tensor is evaluated by pushing it forward using a vector field and then we transform (pull back) the coordinates so that the shifted point has the same coordinate labels as the old point."

no longer makes sense to me

given this

Ryder Rude

10:16 AM

in physics, pushing forward everything on the original manifold is part of diffeomorphism

in mathematics, diffeomorphism is just a smooth map between manifolds

let's say the math diffeomorphism is a map between manifolds, and the physics diffeomorphism is a map from a manifold with tensor fields to a manifold with tensor fields

ACuriousMind

@lucabtz yes, I noticed the D-module/monodromy connection

Ryder Rude

in math, a diffeomorphism is an equivalence relation on smooth structures. in physics, a diffeomorphism is an equivalence relation on smooth structures with tensor fields

ACuriousMind

10:33 AM

@qwerty I think this is a confusing way to talk about things, and it is caused by physicists being unable to talk about anything without using coordinates :P

A diffeomorphism is just a smooth invertible map $f : M \to M$

a coordinate chart is a smooth invertible map $\phi : U_i\to M$ for some $U_i\subset \mathbb{R}^n$

what the snippet you quote there is trying to say is that they're applying the diffeomorphism $f$ to $M$, but then using $f\circ \phi : U_i \to M$ as a coordinate chart - the image $\phi(U_i)$ gets "shifted" by $f$, so the "same" coordiantes now denote different points

naturallyInconsistent

@ACuriousMind it should be the other way around, $M\to U_i$

ACuriousMind

@naturallyInconsistent different conventions are possible; since the map is invertible (on its image) it doesn't matter which direction you call the chart

Ryder Rude

@naturallyInconsistent this is incorrect. the chart is not defined on all manifold points

in $\phi _i : U_i \rightarrow M$, the map need not be onto

it is onto for a subset of $M$

ACuriousMind

the first sentence about "a combination of coordinate change and pushforward is a diffeomorphism" is also a mathematical nightmare, but what they mean is that if you look at $f$ in terms of your new coordinate chart $f\circ \phi$, what's happening is that you just "changed the coordinates" by shifting $\phi(U_i)$ around but all your tensors additionally changed through $f$s pushforward

naturallyInconsistent

@ACuriousMind I know it is invertible so that it is somewhat doesnt matter. My point, however, is that there is a unique $c\in U_i$ that is selected by each single chart for every $p\in M$ (where the chart is defined over) whereas for the inverse function, we often extend its domain of applicability by identifying, say, $\forall n\in\mathbb Z\qquad2n\pi=0$

@RyderRude stop replying to my stuff.

ACuriousMind

10:43 AM

@naturallyInconsistent I'm not sure what you mean. Perhaps the issue is that what we often casually call "coordinates" are not actually coordinate charts in the proper mathematical sense, e.g. $\mathbb{R}\to S^1, x\mapsto \mathrm{e}^{\mathrm{i}x}$ is not a coordinate chart - the circle needs at least two charts to be covered

naturallyInconsistent

@ACuriousMind yes, I am also aware and was trying to allude to this

ACuriousMind

maybe the issue is that I should have also written the target as $V_i\subset M$ when I said the map is invertible?

naturallyInconsistent

@ACuriousMind that is to reply to RR. I was not onto that

@ACuriousMind What you have deduced in this comment, is what I was trying to mean.

Anyway, since we are both on the same page here, it is time for meow to exit the convo. It is time for debauchery miehehehe

qwerty

ok, time for me to read through this carefully. thanks for your input everyone.

Ryder Rude

$R$ to $S^1$ is a covering in technical terms

this doesnt have to do with charts. it is defined in the absence of co ordinates

Transcript for