@Kaumudi.H ping ing ing

Have you checked the allowed apps option ?

@anonymous Oh neat, you use it too?

@SirCumference I found the screenshot on the web. I used it few years back

Now I don't need it

@Kaumudi.H Read the steps here exponentialage.com/2014/03/…

@anonymous Something better?

@SirCumference Oh no. I've lost my interest in phones now. I just carry a basic handset (galaxy s6) with almost no extra apps.

I use my laptop for most of the things

@anonymous If you have the StackExchange app and AirDroid, then you can basically see desktop notifications when you get rep or have something in your inbox

@SirCumference I have my laptops open all the time. For the time being I don't really need it :). Maybe sometime in future

@Kaumudi.H @JohnRennie Oh, forgot to mention. When you get a call, you can hang up from your computer or use your computer to answer it on your phone.

@Kaumudi.H :-)

Morning @heather

@heather hey :)

@SirCumference hello

@anonymous hey =)

A lot happened while you were away :D.

ACM finally agreed

We found a road named "John Rennie"

And we found JR's address too :P

@anonymous (kidding)

wow

I'm gonna give him a surprise visit :D

@anonymous with what?

@heather With our stand on the politics issue

@anonymous =D =D

@anonymous Which was?

@Kaumudi.H ...how?

Oh

@Kaumudi.H Well, now even I do :D...I'm gonna rob his house and all his laptops probably!

Wait, no, I don't remember that

That's neat tho

@Kaumudi.H Wait, why?

Oh, wow

JR is the new Santa

@anonymous I don't, personally, agree with your stance. But that doesn't matter, as I said, since there is clear community resistance against the "no politics policy", there's no point in enacting it - acting against the express will of the community is not what moderators are elected for. The meta post will be updated shortly to reflect that the policy outlined there should be considered obsolete.

@SirCumference The beard is a bit short for that, though

@ACuriousMind Nonsense

Okay, I'll stop photoshoping people here

My goodness ^^^^^^^^^^^^^^^^^ :D

I don't know why, but most pictures are considerably improved by a Rennie-face :D

@SirCumference I'm closing my eyes and imagining him doing "HO HO HO" :D like normal santas ! I can't stop laughing now :)

"like normal santas"...so John is an abnormal santa?

@ACuriousMind I don't think Santa's British. He's from the north pole.

@ACuriousMind Obviously. Only abnormal santas can mail a laptop all the way from Europe to India to an unkown person on the Internet :P

@SirCumference Well, aren't the British known to be a bit...*frosty*?

VICTORY IS OURS

@Kaumudi.H :-)

@Kaumudi.H we actually know JR's address too but we deleted it

anonymous actually posted it up but he deleted it due to peer pressure

yeah it is a simple google search away

@Kaumudi.H Sorry if my latency is a bit high at the moment but I'm dismantling three laptops!

@ACuriousMind To be honest, the original wasn't too far different

Round glasses, goatee

goatee?

Or, I dunno the kind of mustache that goes down

Neither John's profile picutre nor that man have a goatee

Fu Manchu is the name

Not goatee

:-)

@Kaumudi.H still wishes SE had a PM feature

Re-assembled one of the laptops - two to go now.

don't worry

physics.qandaexchange has a PM system and JR is on there

@Kaumudi.H Actually I have the link to his Google plus/Youtube profile. I can send a mail directly using that to his gmail :).

gmail allows mailing google plus users

I have JR phone number so beat that

So do I ^

lol

JR is in danger of foreign invasion :).

@Kenshin My landline goes to an IVR system to deter spam phone calls. You can ring it, but all that will happen it the system sends me a voicemail.

So sad :(. Now I can't call (to warn you) before I rob your house :P.

@JohnRennie do you check voicemail?

Occassionally :-)

then it's sufficient

@Kaumudi.H Everybody has his address. It takes just 5 seconds to find it :P

@Kaumudi.H I read that as "I didn't do any stalking yet" o.O

@HDE226868 I think you might find this cool too

Astronomers discover the first white dwarf pulsar in history, ending half a century of searching

@SirCumference That's interesting. I was aware of the system and of pulsations by the white dwarf, but I didn't know that the emissions were polarized.

@HDE226868 I hadn't actually heard of the system, so I might be a bit more surprised

@SirCumference It turns out I wrote an answer about it.

Maybe it deserves an update.

@HDE226868 I had actually upvoted that answer. Guess I forgot about it :P

@SirCumference I wasn't

@ACuriousMind What's the usual reference for infinite dimensional projective unitary reps?

Has Dufflield gone insane?

@0celo7 I'm not sure there is such a thing, but my course on the reps of the Poincaré group used a large amount of rep theory due to Mackey

@JamalS Please refrain from discussing chat-banned users in the chat room (and also from calling any user "insane", regardless of how justified you think it is)

@ACuriousMind I didn't know he was banned - is there a list to see chat-banned users in order to refrain from mentioning chat-banned users?

@JamalS No, there isn't (that'd be a pillory-type feature which SE decidedly doesn't want)

@ACuriousMind Hi. May I ask you some question in relation with your answer to my question, so to save from posting them as comments? If you have time of course and I am not bothering you.

Mentioning them is also not usually a big deal, but criticizing someone in a public place where they cannot reply at all is questionable

@ConstantineBlack Sure, ask away

@0celo7 if I have a disconnected manifold, what would be the proof that a PDE's values on one component are unaffected by values on another component

Can I consider an argument such as your second paragraph in relation with the posted Lagrangian? Assuming the existence of QCD as the fundamental theory, all the phenomenological low energy models are but mere approximations; so the pions may be a meaningfull way to capture the dynamics of the NN interaction phenomenologically but are completely meaningless if one tries to interpet them as actual free states, since the dynamics of their interaction cannot be modeled by this Lagrangian.

Then 1) how could I “explain” this based on Chiral Perturbation Theory or QCD and 2) is there a way to extract such results from the already given Lagrangian and the phenomenology?

@Slereah you need to be more precise with "unaffected"

The class of solutions on one component does not depend on the solution in another

It would depend on your actual problem and precise existence/uniqueness result.

@ConstantineBlack No, this type of information is somewhat external to the Lagrangian. The pion-nucleon interaction Lagrangian is designed to be a good approximation to the residual nuclear force (and hence the interaction of nucleons with each other), but it is not designed to be a good approximation to scattering of pions.

Boundary value problems are different from initial value ones.

I'm just looking for a good argument for the connectedness of the spacetime manifold :(

My current one is that path connectedness implies connectedness

Was wondering if there was also a theorem regarding PDEs

@Slereah By restriction, a solution on the whole gives you solutions on the connected pieces. By disjoint union, solutions on the pieces give you a solution on the whole. These maps are inverses of each other, so giving a solution on the pieces is equivalent to giving a solution on the whole. Is that what you mean by "unaffected"?

Well what I want to say is a bit hard because obviously you can't have a time coordinate that makes sense for two disconnected pieces

@ACuriousMind So indeed, I can argue that based on the experimental phenomenology the pions are meaningless as free out or in states, even if there is no problem mathematically. Is this statement correct?

So I can't really talk about initial value problem

@ConstantineBlack yes

Hm, how to express this

Maybe

Well, actually, I'm not sure how bad the result for the pions from this is, but I'm guessing it's pretty bad.

In R^n, the usual theorems are formulated for domains

Which are connected by definition

The class of solutions for the component of a disconnected manifold is the same as the class of solutions for a single connected manifold equal to that component

(assuming the PDEs aren't pathological)

For instance potential terms that depend on values in disconnected pieces

@ACuriousMind And that's where ChPT comes into play? Allowing us to interpret as much better as we can the subject of low-energy QCD. From there, as I have read, we can build the effective Lagrangian for all types of interactions. Agree?

@Slereah that sounds horrible

Why do you have nonlocal potentials?

@0celo7 Yeah hence why I discard such possibilities

Well I don't

I specifically said nothing pathological like that

@ConstantineBlack Yes, chiral perturbation theory is "the" low-energy effective field theory of QCD

I'm sure there's a theorem like that somewhere

But I dunno

Sounds harsh to prove

what are we doing

@ACuriousMind :) I knew that. Thank you very much for your time. It still feels a bit weird, not to be able to make arguments about the phenomenological Lagrangians from within the theory; at least argue why only some amplitudes have meaning and others don't. Anyway, if don't have anything else to add, thank you again for your consideration. Be well.

@ConstantineBlack Consider that it is the same even for classical approximations: Consider the pendulum - once you have made the small-angle approximation, you can't tell from the small-angle theory itself that it is only valid for small angles.

that is, this is no special feature of quantum field theory, it's an inherent feature of most approximations

@0celo7 Oh, you suddenly entered the chatroom at 4am

@ACuriousMind Indeed, that makes sense. I was wondering more on the possibility that we could show something from within this particular QFT that would allows us to explain why pions remain meaningfull only as exchangeables. But as you put it, that's impossible by construction of the model. Right? I cannot phrase an argument like " this happens and so pions remain internal in this model", since mathematically there is no problem for them being external legs.

@SirCumference my phone does that when I forget to close chrome

@ConstantineBlack Yes, that's how I see it.

@Slereah If you have any nonlocality you can't apply the classical theory

Are you even reading me

@ACuriousMind OK. As I said, be well and thank you. Good day.

I am specifically excluding such non-local things

errything is local

@ConstantineBlack You too have a nice day, bye!

@Slereah I mean nonlocality in a connected component

There's no guarantee your nonlocality can be contained in a single chart

Even in a connected component

I just want nice well behaved PDEs

And you're working with a messed up signature. Is your equation hyperbolic?

This section is normal spacetime

So signature (-+++)

The superior signature

I think you need to get that book Valter mentioned on wave equations on manifolds

I do have it somewhere

Legal copy?

What's the name again

Although I doubt it mentions that thing

All my copies are legal

I'm a good boy

arxiv.org/pdf/0806.1036v1.pdf

this?

200 fucking pages

More reading

Hm, I wonder how easy it would be to prove the equivalence between the tangent bundle and the usual definition of tangent space

The tangent bundle and the tangent space are not equivalent... ?

The former is union of all the tangent spaces

Well in some sources, the tangent space is defined via the tangent bundle

^I, too, wish to register my confusion about that statement

in other sources, it is defined by the tangent vectors of curves

@Slereah ...and how do you define the tangent bundle without defining the tangent spaces?

Maybe there's a categorical way of constructing TM

Well definitely make that go away

@ACuriousMind curves

@0celo7 That's how you define a tangent space in the first place.

You'd define the tangent space too

@0celo7 Fear not, the good people of the nlab have you covered

You can define the tangent space as just fibers of the tangent bundle

@BalarkaSen you could jump right to the bundle by saying your curve gives (p,v)

Just a thought

I'm not saying @Slereah is making any sense, mind you

You traitor

Sure, but the two things aren't very different. I don't see how to make the notion of tangent bundle more fundamental than tangent spaces

@BalarkaSen 100% agree

I reiterate: Sam did not take his meds

@Slereah That's circular unless you have an abstract characterization of the tangent bundle, is what we are trying to say

I'm not saying the proof would be terribly difficult

@ACuriousMind lol

Maybe it's like the space of stalks of the sheaf of smooth functions on the manifold or something dumb like that

Is that how Bredon defines it?

yeah I don't want to go that abstract, either :p

He defines smooth structures like that

I think so

Or in that spirit anyway

@ACM Ah, so it's the internal hom of the space of infinitsimals into the manifold. Got it

In the category of smooth topoi, of course

Trivial!

@SirCumference I always thought pulsars are too heavy to be anything other than neutron stars, that sure is an interesting finding

Sometimes you have weird happenstances

Like dead stars vampirizing other stars and such

@0celo7 Of course! This is just because smooth manifolds are differential 2-topoi

@BalarkaSen Slereah really should have thought of that.

I agree

"It is shown in §12.11 that the covariant and contravariant tangent bundles are equivalent"

I don't think i'll survive that many chapters of Steenrod

Who calls them covariant and contravariant? Wait, you're reading Steenrod?

He probably means the cotangent vs tangent bundle

Well yes

Because I own it ( ͡° ͜ʖ ͡°)

@BalarkaSen certainly. But still an old terminology

mhm

Steenrod is pretty old

Why are you reading him?

I wonder what he means by "equivalent".

(his fiber bundles book, right?)

isomorphic as smooth vector bundles, surely.

yes

Well you see

@BalarkaSen well that's not too interesting

Steenrod is some kind of antique book of GR

Because it contains the One Proof

That nobody will ever do again

What's the theorem?

@0celo7 Such an isomorphism is the same as a choice of a Riemannian metric!

The theorem that for a compact manifold, the existence of a Lorentz metric is equivalent to the existence of a vector field

Meanwhile, in an alternate universe: Da h bar [contains profanity]

I'd like to understand it someday

It involves homotopies on bundles and deformation retractions

And like 4 different bundles

@BalarkaSen I know. I love riemannian geometry but that's still not interesting

@Slereah Interesting; what's a Lorentz metric?

I once proved there is no natural transformation taking TM into T*M

Don't remember how I did it

Bilinear symmetric form of signature (1,n)

I don't understand; natural transformation of what functors?

Functor? I hardly know 'er

@BalarkaSen tangent and cotangent functors

From Diff to VB

I think.

What do those functors do?

Eats what, spits what?

Eats manifold, spits out the bundle, I think.

You're making me question my life choices now

Ohh. I see.

I'll look it up later to be sure

No, you're right, I was being silly.

Why do you need a functor for that

Can't you use a boring old function

Instead of breaking out the categories

@BalarkaSen i have a book on functorial diff geo. I didn't get far because it's scary

I think we've talked about it before

That does make sense; the point should be that there is no One Riemannian Metric out there

I don't know a quick proof though

I'm doubtful of your claim that an isomorphism gives a Riemannian metric.

Because Lorentizan metrics also give an isomorphism.

An isomorphism TM --> T^*M is the same as a map TM otimes TM --> R. I guess you need positive definitness for Riemannian is the point

Yep.

Got it

Thanks.

Also symmetry?

Right, right.

@BalarkaSen Now I want to take another crack at that book

hm

by the Steenrod thing

's too hard for me

You need a p-form for a metric of signature (p,q)

Does that mean that if you have a nonzero vector field on a spacetime, you also have a nonzero pseudovector field

Since for most things (1,n) ~ (n,1)

@Slereah Sure, apply Hodge duality.

Makes sense

uu.diva-portal.org/smash/get/diva2:531162/FULLTEXT02.pdf

A much better place to learn about the ol' bundle

that sounds like physics

if you want to learn vector bundles i recommend Hatcher's notes

@anonymous Should you have any other questions please let me know.

Physics is best

At least they tend to motivate a construction

They don't throw around ten structures of mysterious use

Yeah, I understand that. But it's their nonrigorous handwaving mathematics that I have any personal beef with, is all.

I too hate mathematics robbed of intuition

Physics is of various mathematical rigor

Just ask @0celo7 his opinion on physic's rigor in QM

I almost get into an embarassment with my supervisors when I send some computing application form for them to fill in, and stupid outlook owa attached an irrelevant pdf attachment even though it says it has deleted that attachment. Luckily of the 9 pdfs of which 8 of them will be a total disaster if attached instead, the mis attachment happens in end up in the only one pdf that is not my scribbles, thus won't get me into embarassment trouble because it has a formal context

I don't understand why uni mailing systems love to use outlook instead of gmail

Star Trek TOS has an embarassing amount of planets almost identical to earth

I don't remember earth having that many plastic rocks ;)

Well there's a planet with a roman empire

A nazi planet

A gangster planet

A planet with americans and soviets

It gets a bit embarassing

Anyway, to completely knock out those "quantum trajectories" in the future that will end up repeating the same mistake again (or worse), I have moved away all the 8 other irrelevant pdfs from my folder and to remind myself to delete any draft should I found I misattach a file when writing the email as I know my uni's outlook will probably fail to delete it again

Also if you think plastic rocks are bad

Do you remember the second episode

Look at that quality matte painting

Heh

My favorite cheap prop remains the space dog

they were too cheap to get a lizard puppet

so they made a space dog