The h Bar

Danu

21:00

@BalarkaSen Sigh, yeah I guess

Balarka Sen

@Danu Cool. What did you learn?

user507974

wait... what direction was pressure in the thermodynamic entity

Danu

@BalarkaSen Everything up to ch.4

Minus the Hopf degree theorem and everything in its section---I just looked at the results.

Balarka Sen

@Danu Oh, really?

Danu

I didn't do many exercises. I'm under very high time pressure.

0celo7

21:03

Danu is a speed reader

Balarka Sen

@Danu Ah, that explains it. Fair enough.

Danu

But the exercises don't seem so bad, tbh.

Balarka Sen

There are many cool ones.

Danu

I feel like I should be able to do most of them quickly

Balarka Sen

Well :) If you can, that's good.

Danu

21:04

@0celo7 If only that were a thing for mathematics :P

Balarka Sen

Do you want a problem to think about? I have one which I haven't solved in full yet.

Not from G&P, but relevant to ch.2

0celo7

@Danu Exercise: Solve the Riemann hypothesis.

trilolil

Hello everyone, very quick and easy question regarding waves accross materials

someone hits the rod with a hammer and a wave propagates accross it:
www.imgur.com/0mGs3sI

on the second line, nex to the arrow you see $F=\Delta p - S ....$
I think both terms should be switched, because I think right now the force F will always be negative, and I am not sure whether that makes any sense. Could anybody concur?

0celo7

@BalarkaSen what's the problem

Balarka Sen

Don't bother with it. I was just going to tell it to Danu in case he's interested.

0celo7

21:09

...why can't I hear it?

user507974

@0celo7 cuz he is probably in a different state or country as you

0celo7

@user507974 Ha-ha.

He's on a different continent than @Danu , too.

Balarka Sen

I don't get the joke.

0celo7

hear

you're far away so I cannot hear you

trilolil

was there a joke?

c'mon guys I want to laugh as well

Balarka Sen

21:14

@0celo7 That's not even a joke.

trilolil

who are you speaking to?

Balarka Sen

I mean, neither are my jokes anyway.

user507974

@BalarkaSen tough crowd

@0celo7 at least i got one person who enjoyed it

0celo7

@BalarkaSen I'd like to hear the problem

trilolil

I'd like to hear the joke

Balarka Sen

21:16

@0celo7 OK.

0celo7

@trilolil Ed Witten's voice

Balarka Sen

It's the 4 dimensional smooth Poincare conjecture.

0celo7

isn't that still out for grabs?

trilolil

ok now that I have your attention:

very quick and easy question regarding waves accross materials

someone hits the rod with a hammer and a wave propagates accross it:
www.imgur.com/0mGs3sI

on the second line, nex to the arrow you see $F=\Delta p - S ....$
I think both terms should be switched, because I think right now the force F will always be negative, and I am not sure whether that makes any sense. Could anybody concur?

0celo7

@trilolil I'm not a physicist

trilolil

21:17

@0celo7 yhea but I know u can solve it

u r that mathemagician guy

0celo7

...who are you?

trilolil

a student

who s trying to understand his textbooks

0celo7

@BalarkaSen so what about the conjecture

Balarka Sen

it is the problem.

0celo7

you're trying to prove it?

Balarka Sen

21:22

yup

0celo7

what're your thoughts on it

Balarka Sen

i am pretty close

@0celo7 can't tell you; it's a matter of fame and money

Secret

Last night dream is extremely QFT heavy in theme (yet when you actually read through it, it is actually more possibly, me trying to understand QFT subconsciously in my sleep, because it is nonsense when you cross check with actual QFT knowledge)

The dream begins with an expression floating in a white void and then the camera pan from left to right $\int d^3x \tilde{f}\partial g(x)$. It then fade into a scene where there is a bessel function like wave travelling to the right and with amplitude decaying exponentially as it passes thorugh the middle of a black horizontal line.

Balarka Sen

secrecy is important

0celo7

@BalarkaSen are you trolling

Balarka Sen

21:23

I was. But I gotta go now.

0celo7

@Secret Jesus. Are you OK?

Secret

@0celo7 I am not sure, possibly it means it is a very bad idea to try to understand the LSZ reduction formula at 4:00 am in the morning...?

Danu

@BalarkaSen Tell me

I was just away

Balarka Sen

@Danu Take a submanifold $N$ inside a big manifold $M$. You're aware of the relation between self-intersection of $N$ and the tubular nbhd of $N$ in $M$?

Danu

No.

Balarka Sen

21:27

If not, exercise (1) if tubular nbhds of $N$ is trivial in $M$, then $N$ has self-intersection (by which I mean the intersection of a perturbed copy of $N$ in $M$ with itself) is null.

Danu

What do you mean by a tubular neighborhood being trivial

A product?

Balarka Sen

Yes, it's the product of the disk with $N$. The trivial bundle.

Or equivalently normal bundle is trivial. Whatever you prefer.

Danu

Okay, that seems very straightforward

You know just perturb it inside the disk

0celo7

@BalarkaSen oh come the fuck on

Balarka Sen

That's it.

0celo7

21:29

why wouldn't you tell me

Balarka Sen

Exercise (2) suppose $\dim M = 2\dim N$. is the converse true?

Danu

@BalarkaSen Not sure

If $\operatorname{dim}M=2\mod 4$, then do you have any example of something with a nontrivial tubular neighborhood?

Because if $\operatorname{dim}N$ is odd then it always has null self-intersection.

So that'd solve your question (in the negative)

Balarka Sen

@Danu Eh? Circle inside moebius band. Moebius band has dimension 2 (= 2 mod 4), circle has dimension 1, which is odd.

Or compactify that to RP^2.

Danu

Sorry, forgot orientability.

You need orientability

It's funny: I went through this line of reasoning 3-4 times in the past week

Every time I kept on thinking WTF MOBIUS BAND

and after a few minutes I remember orientability

So if $M,N$ are both orientable

You get a counterexample

Anyways, so you think it's true @BalarkaSen?

Balarka Sen

@Danu Why's this true, modulo orientability?

@Danu I don't. I have a counterexample, but I am not happy with it.

Danu

21:36

@BalarkaSen G&P

Balarka Sen

Exercise (3) pull up the smallest dimensional counterexample you have.

Danu

Section 3.3

I don't have a counterexample

0celo7

In section 3.3 they work exclusively with oriented manifolds.

Danu

I just gave you a perhaps simple way to find one

Secret

What are the dimensions of the klein bottle and RP^3 (the first being non orientable while the second is)?

Danu

21:37

@Secret 2,3

Disregard 0celo7's comment: What I said is true.

0celo7

@Danu Self-intersection being 0 for odd dimensions only works in the orientable case because the proof uses orientable intersection.

Balarka Sen

@Danu Are you sure? Oriented self intersection is different.

Danu

5 mins ago, by Danu

So if $M,N$ are both orientable

0celo7

Then yes.

But you said that after the comment @BalarkaSen asked about.

Danu

And Section 3.3 explains exactly why it's true, modulo orientability

Stop trying to correct me?

0celo7

21:41

What do you mean by modulo orientability

Balarka Sen

Oh, of course it's true. Nevermind.

OK, yes, so I guess you can come up with a counterexample out of this. I hadn't thought of this.

But I still want to see a small dimensional counterexample :)

I have a ctrexample in dimension $4$, but with disconnected submanifolds.

Secret

How about a torus and a circle inside it (both orieintable, torus has dimension 2 while the circle has 1)?

Balarka Sen

Circle has trivial normal bundle.

There are no 2 dimensional example.

Secret

ok

Danu

@BalarkaSen Ah, you know that already?

Balarka Sen

21:43

You can check that by hand.

Danu

How to do so for non-orientable?

I believe it for connected sums of tori

Balarka Sen

Non-orientable 2-manifolds are connected sum of RP^2's.

Secret

e.g. klein bottle is RP^2 # RP^2

Balarka Sen

I guess my disconnected counterexample descends to a counterexample in dimension 2, but that's not interesting.

Danu

@BalarkaSen You know I know that :P I want to know how you do it in RP2, of course.

Balarka Sen

21:46

Any two circles in RP^2 intersect at a point.

That's by the cohomology structure of RP^2.

Danu

There you use the correspondence between intersection theory and cup products huh

Balarka Sen

Yup.

Danu

Fine

Emilio Pisanty

omg, this is the mother of all minor edits ever

physics.stackexchange.com/posts/274777/revisions

Danu

@EmilioPisanty lmao

0celo7

21:48

nice

TeX purity is indeed a worthy goal

Danu

That must've started as an intention of editing something else.

Balarka Sen

Also, is there a 3-dimensional example? Can a surface have trivial self intersection in a 3-manifold if it has nontrivial tubular nbhd?

Danu

Dunno, broski

Balarka Sen

That is le problem.

Danu

The real question is

whether I can breeze through ch. 4 of G&P in 1-2 days :P

Balarka Sen

21:50

You're being an 0celo reader.

0celo7

@Danu If you know how to integrate forms, that's most of it.

@BalarkaSen Huh?

I read GP over ~3 weeks and did like 40 exercises.

@BalarkaSen Do you know anything about locally constant presheaves

Balarka Sen

No. But what do you want me to know?

0celo7

I figured it out.

Balarka Sen

I wish I had more time to do math.

Secret

is there any relationship in regard to your question if I have a torus and I pick a trefoil knot in it (since the trefoil knot can never be unwind into a circle)?

Balarka Sen

21:58

It self-intersects trivially.

Just translate it a bit along the meridian.

Danu

@BalarkaSen The worst of insults :P

0celo7

Apparently I'm now an insult

Balarka Sen

@Danu I know!

Danu

"now" :P

0celo7

@Danu You're being a bully again

Danu

22:00

@BalarkaSen Principles go out the window when thesis supervisors ask things

Gotta go sleep now---bye

Balarka Sen

True, I understand.

Bubyes.

@Secret I misspoke: what I meant to say is, it has trivial tubular neighborhood (hence obviously self intersects trivially).

Working with torii and stuff would be of no use.

Things will always have trivial tubular nbhd there.

You want something which doesn't have trivial tubular nbhd yet still self intersect nontrivially.

0celo7

@BalarkaSen We've talked about that "differential algebraic topology" book, have you looked at it any?

Not that I need it

Just wondering what it's about

user507974

22:22

@EmilioPisanty lol

dmckee

@0celo7 A gen-ed descriptive astronomy class that I'm having to make up as I go, the first semester of our algebra/trig based intro class for non-majors (at night), and modern physics for the juniors.

Should be a busy, but fun time.

0celo7

three classes?

I can't imagine a prof at my school teaching three classes

dmckee

@0celo7 It is a teaching school.

Major research places typically have 1/2 -- 2/3 of the load I teach.

That's one of the things that makes it hard for me to get much research done.

Trying to get the astro class sorted out has pointed out the degree to which I am not an astronomer.

There is a lot of implicit knowledge about interconnection in the subject that goes into planning courses, and I've having to work it all out explicitly. Ugh.

0celo7

dumb question, but how do you do hep-ex research at a university which doesn't have a dedicated lab for it (presumably)

dmckee

On a toy scale. And I'm trying to branch out a bit.

These projects are as much learning environments for the students as science for its own sake.

0celo7

22:36

@BernardMeurer I need your advice

dmckee

@0celo7 IN the re-model that is currently going on we're going to get a tiny little lab space for the four of us to share. But its better that what we had before (i.e. no lab space).

0celo7

Yikes

@dmckee We share a lab with some people and we want to kick them out because our group is getting larger

11 people for 6 desks is not good

But they have equipment that cannot be moved, so it's not going to happen

Emilio Pisanty

@dmckee Given that, I guess I shouldn't mention that I'm currently working in a lab that's been converted into a theory office, then.

Has a big shiny "Laser Active" warning light on top of the door and everything.

DanielSank

Hi, everybody.

0celo7

@DanielSank Hello

DanielSank

22:48

Hey, I wanna understand how to actually use path integration to do stuff.

ACuriousMind

@peterh Do not use the edit button in the close review queue (as you did here) unless your edit changes the question in a way that makes the close votes obsolete. It's stupid that this option is even there, and even more stupid that it single-handedly completes the review, but you shouldn't use that edit button unless you address the reasons for closure, cf. e.g. this answer by Shog9.

4

DanielSank

The closest I've found to a not terrible book is Altland and Simons.

Anyone have a better?

I really want something that explains the mathematics thoroughly, but not necessarily with every epsilon and delta.

0celo7

@ACuriousMind I don't see what the issue is.

DanielSank

@ACuriousMind Yeah, seriously, that option works in unexpected ways.

ACuriousMind

@DanielSank Depends which stuff. I know you can do stuff with it on lattices, or you can do stuff with it for non-equilibrium theories, and possibly more...

0celo7

22:49

What does "single-handedly completes the review" mean?

ACuriousMind

In all cases the techniques used to evaluate the integral are rather different

DanielSank

@ACuriousMind Mostly I want to be able to understand the way that Caldeira and Leggett describe the effect of coupling to an environment.

Emilio Pisanty

@DanielSank Honestly, it sounds (a bit) like you're asking for the Moon on a stick there

DanielSank

Generally, when entering into a new area like this, I prefer to lock in the mathematics first.

@EmilioPisanty I doubt that.

ACuriousMind

@0celo7 It means that instead of the close votes or three reopen votes to take the question out of the queue, the close vote review is stopped immediately after the edit

dmckee

22:51

@0celo7 It normally takes three "leave open" votes to remove a question from the close review queue while leaving it open. The edit option bypasses that.

ACuriousMind

@DanielSank Are we talking about a path integral in QM or in QFT

DanielSank

@ACuriousMind I remain unconvinced that this really matters.

0celo7

@dmckee You can leave a question open by simply editing it?

DanielSank

but we can start with QM

Emilio Pisanty

@DanielSank Maybe give Schulman a spin?

ACuriousMind

22:51

@DanielSank In QM you can find a mathematically rigorous foundation with nice analogies to e.g. Brownian motion. In QFT no rigorous foundation is known.

So it matters a lot

Emilio Pisanty

store.doverpublications.com/0486445283.html

dmckee

@0celo7 You are suppose to fix the problem with it. Editing without fixing the problem is very poor form.

ACuriousMind

Infinite degrees of freedom really are a bitch to integrate over :P

Emilio Pisanty

amazon.com/Techniques-Applications-Integration-Dover-Physics/dp/…

DanielSank

@EmilioPisanty Looks nice.

Cheap too.

@ACuriousMind Really?

0celo7

22:52

@dmckee so you can no longer close it once it's edited?

Emilio Pisanty

@DanielSank Yeah, it's worth a shot with not a lot to lose

I can't say I've used it that much though

0celo7

@DanielSank I'm filling my glass early.

DanielSank

@ACuriousMind I can show you a lot of math lacking in rigorous foundation but which still makes sense and works.

ACuriousMind

@0celo7 You can, but it is no longer in the review queue until someone casts a new close vote on it manually.

Emilio Pisanty

I did find his treatment of a particle on a ring quite amusing, though

DanielSank

22:53

@0celo7 I have no idea what that means.

@EmilioPisanty Well that's a good endorsement XD

Emilio Pisanty

@DanielSank hang on, I'll find it

ACuriousMind

@DanielSank The issue is more that it's so ill-defined that no one could tell you how to compute a generic QFT path integral. But for any specific case, you'll find a lot of people knowing the correct trick to reduce it to a better defined integral.

DanielSank

@EmilioPisanty here is an example of what I consider explaining math thoroughly but without epsilon and delta.

@ACuriousMind That is all I care about!

I am perfectly happy to use fundamentally ill-defined tricks as long as they make sense.

Emilio Pisanty

> The degree of pathology exhibited by this Green's function is entertaining, especially in view of the elementary nature of the example.

dx.doi.org/10.1103/PhysRev.176.1558

DanielSank

Switching limits without justification? No problem! This is physics!

0celo7

22:55

@DanielSank Getting books on sale while the getting's good even though I won't open them for a while

ACuriousMind

@DanielSank Yeah, but the point is that there's - at least to me - no pattern to these tricks. You're not learning things about the path integral, you're learing things about the specific physical situation you're evaluating. Which surely also is nice, but I wouldn't say that qualifies as "explaining the mathematics throughly"

DanielSank

@EmilioPisanty ~sigh~ no access.

Emilio Pisanty

@DanielSank Well, it is a Sunday

DanielSank

@ACuriousMind Well, my relatively uninformed opinion is that you're wrong.

Emilio Pisanty

have you got Phys Rev access through Google?

0celo7

22:57

@EmilioPisanty I believe that is done in Shankar

(path integral for spin)

DanielSank

I estimate that there is intuition to take away from these tricks.

Emilio Pisanty

@0celo7 That's not my main interest in that paper TBH. I was after the Fourier series for the propagator.

Secret

@DanielSank I like how you give a physical notion to nearly every step of the maths, which does help alot in visualising what compelx contour integration is doing

DanielSank

@EmilioPisanty Not quite. Google has company-wide access to IEEE and similar, but not APS. We have a specific setup to access APS but it hasn't worked in a while because of some issue with our network configuration.

Emilio Pisanty

Turns out it's really, really badly behaved.

DanielSank

22:58

It's annoying.

@Secret Thank you. Are you aware, by the way, that contour integration is just a special case of Stokes's theorem and/or the divergence theorem for vectors?

I have written about this before, and can find the link if you like.

0celo7

@DanielSank Do you mean Cauchy's theorem is?

/residue theorem

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