The h Bar

WillO

01:48

Slearah: I don't have Steenrod in front of me so can't tell if he's using some offbeat definition (maybe offbeat today but not in his day?) but by the usual definitions, every tensor bundle is a vector bundle, for sure.

Yuvraj Singh...

04:29

Lol

Last one for acm

skullpatrol

04:52

lack of research @YuvrajSingh... Pal

Yuvraj Singh...

Boomerang @skullpatrol

skullpatrol

lol

Guru Vishnu

05:47

Hi. Can anyone tell what is wrong with the following method of computing the effective capacitance between two points (marked with red circles)? :

I got the effective capacitance as 2C when I considered the system to be a combination of balanced Wheatstone network and a capacitor connected in parallel with the terminals. And it's the correct answer as per the book.

Secret

06:40

I recall I turned the lightbulb joke into an actual conspiracy theory

that the mere act of joking about screwing a lightbulb will eventually caused it to screw itself in, regardless of what the lightbulb is

It's a conspiracy theory because say you identify lightbulb with the US government

Yuvraj Singh...

@Secret joke is quite old isn't it?

Secret

yup

Yuvraj Singh...

Do you have some more?

Secret

nope I am not good at jokes

Yuvraj Singh...

Np, do you mind I am talking to you for some time? I haven't talk much with you since I joined this room!

Are you a theoretical physicist?

@Secret

Secret

06:47

nah I am a computational chemist

currently doing a PhD

I do have a very strong interest on theoretical physics

but I quite suck at it

Yuvraj Singh...

Yes as I can see you on mse

Secret

However, I think more like an artist and philosopher, and get sentimental

Yuvraj Singh...

A strong mathematics students would definitely be good in theoretical physics!

I believe *

Secret

not necessary, theoretical physics involves some intuitions as well to use the correct assumptions

Also they have their nonrigorous language that is math like but mathematicians have only starting to understood it

Yuvraj Singh...

Physics is based on how well you can imagine nature working

And you should have mathematics to write that

Guru Vishnu

06:51

Don't need English?

Yuvraj Singh...

@Secret as a student what you feel can be best difference between mathematical physics and it's reverse physics mathematics, since both have included mathematics and physics?

Secret

07:13

mathematical physics is more rigorous, physical mathematics requires a bit of intuition

ACuriousMind

@Slereah I'm not quite sure what counts as a "tensor bundle" here, but there are algebro-geometric analogues of the (co)tangent bundle in form of the (co)tangent sheafs (see e.g. en.wikipedia.org/wiki/K%C3%A4hler_differential), but these sheafs do not necessarily represent a vector bundle - only when they are locally free

@dumbasarock Please don't post links to your questions here directly after you've posted them; if everyone did that the chat would consist of little else.

dumb as a rock

okay sir I won't do that again.

ACuriousMind

You told me you wouldn't call me 'sir' :P

dumb as a rock

old habit

but can you take a look at that question I just need to know that if I am thinking in the right way ?

although I highly doubt it.
it's like there is a gap fit whatever fits(looks like) in

Slereah

07:43

@ACuriousMind steenrod uses tensor bundle to mean fiber bundles that have a rep of GL acting on the fiber

ACuriousMind

@Slereah Then every GL-principal bundle is an example of a non-vector bundle with such an action, right?

Slereah

@ACuriousMind gonna need to check the definition to see if that fits

dumb as a rock

:-(

Slereah

@ACuriousMind Are magnetic monopoles instantons, or something similar?

From what I can see they don't seem to be, but they're usually grouped in in the same bag

ACuriousMind

@Slereah see physics.stackexchange.com/a/167160/50583

They're not instantons, but they are non-trivial bundles

Slereah

07:58

I'm not 100% sure what instantons are since I'm not sure the definition is standard, but it seems to be related to the third homotopy group of the bundle

And that is trivial for $U(1)$

@ACuriousMind Is there a name for the thing that covers all of them?

outside of "non-trivial principal bundle"

I tried looking it up on ncatlab but they started using the word "gerbes" and then I just woke up covered in blood

ACuriousMind

not sure

but btw I think I figured out/remembered why in classical physics you can't "switch the bundle" - there is no smooth way of doing so, so the equations of motion won't ever evolve an $F$ that comes from one bundle to an $F$ that belongs to another

Slereah

Speaking of that

ACuriousMind

But in QM, we just enumerate all the states and do the path integral, there isn't such a "smooth geometry transition" requirement there

Slereah

One of the standard example for instantons is apparently the $\mathbb{Z}_2$ $\phi^4$ theory, of domain wall fames

Is that a bundle theory?

@ACuriousMind Yes I suspected why that was the reason why it was more important in QM

ACuriousMind

@Slereah that's because people change all the time whether some things should be called "solitons", "instantons", etc...

Slereah

08:09

Yeah they do seem to be playing a bit loose with the term

Are all (non-trivial) instantons also solitons?

They do seem similar since they have topological charges

ACuriousMind

Since I've never seen a good definition of a soliton that didn't involve a good measure of "I know it when I see it" I can't answer that :P

Some people use the interchangably

Slereah

@ACuriousMind Well I can think of one, but I'm not sure it's at the same level of rigor as instantons being the third Chern class of a principal bundle

ACuriousMind

Some people say "soliton" for spatial configurations and "instantons" for temporal configurations with similar topological characteristics

Slereah

Something about $$\lim_{t\to\infty} \phi \neq 0$$

ACuriousMind

@Slereah The rigorous definition for "instantons" I'd use is just "anti-self-dual field strength configuration in a Yang-Mills theory"

@Slereah It's not the "third Chern class". It's that bundles on $S^4$ are classified by homotopy classes of maps $S^3\to G$ (see physics.stackexchange.com/a/127880/50583), and that is the third homotopy group of $G$.

The third chern class would be something like $\int F\wedge F \wedge F$, which doesn't even exist in less than 6 dimensions

Slereah

08:14

By the way, I get that being anti-self-dual can help cast the action in the proper form to show the chern class, but can the field be not (anti-)self-dual?

and if it can, to what instanton sector does it belong to?

@ACuriousMind Isn't that almost the form of the action though?

ACuriousMind

@Slereah The field can, but the classical extremum of the action (="vacuum", in the loose parlance of QFT people) is always anti-self-dual

Slereah

Up to a surface term

@ACuriousMind Ah yes, so it's only the ground state

ACuriousMind

@Slereah Note the three $F$s. The action only has two

Slereah

Ah yes, after checking, the instantion action is three $A$'s

not $F$'s

ACuriousMind

I don't know what the "instanton action" is. Do you mean the Chern-Simons action?

Slereah

08:17

damtp.cam.ac.uk/user/tong/tasi/instanton.pdf

1.6

ACuriousMind

Ah, yes, that term being differentiated there is the "Chern Simons current"

Slereah

Also apparently nlab says you don't need singularities to pretend to have magnetic monopoles, but then they started talking about gerbes again so I died

ACuriousMind

@Slereah What I said above is for the Dirac monopole. There are 't Hooft-Polyakov monopoles that don't have singularities, but involve a larger (broken) symmetry group the EM U(1) embeds in

Slereah

I tried reading up on gerbes but then they started talking about stacks, and the stacks said they were 2-sheafs

And as I'm not quite comfortable with sheafs yet I had to go to bed

It would be nice if there was a bundle simpler than $U(1)$ :p

The $\mathbb{Z}_2$ bundle

But I guess that one has no connection

bolbteppa

@Slereah what about 12.7 of Streater's book, does that seem to say the nlab pre-quantization stuff is a bunch of nonsense?

Slereah

08:29

I mean it's category theory, so of course it is

Also I think Streater was against the usual idea of deformation quantization because it's not an isomorphism

nlab's stuff is geometric quantization, which is I think?

ACuriousMind

Groenewold and Hove say that we can never have a quantization map with all desired properties, so Streater is out of luck :P

Slereah

Well no, because Streater argued for that exactly!

ACuriousMind

@Slereah An isomorphism between what and in what category? :P

bolbteppa

It seems like XVI here is roughly that section of the book

and he mentions Groenewold!

Slereah

Also streater's book isn't saying exactly that those ideas are VERBOTTEN, just that they are well-trodden ground and probably not worth investigating, especially by students

@ACuriousMind The category of prequantum field theories and quantum field theories???

ACuriousMind

08:32

Ah, sure. I'd agree that the vast majority of physicists can live with the ad-hoc inconsistencies of canonical quantization just fine

Slereah

Also really it's not like the "real" quantum theory is usually that weird

If you have a classical $xp$ term, I don't think the quantum theory can be $\pi \hat{x} \hat{p} + e \hat{p} \hat{x}$

bolbteppa

(Funnily enough the end of this mentions the 'oscillator group' which came up in that verbotten question that was asked the other day about when to use oscillators)

Slereah

You can probably just try brute force to check all the reasonable theories :p

skullpatrol

@Slereah have you read S. Coleman, ”Uses of Instantons” in Aspects of Symmetry, Cambridge University Press (1985)?

Slereah

Are there any case where the quantum theory isn't $xp$, $px$, $(xp + px) / 2$ or $((xp))$?

@skullpatrol I have not

Although right now I'm reading about classical instantons

It's hard enough as it is without involving QFT :p

skullpatrol

08:36

hmm

\o @FakeMod

skullpatrol

08:57

XXIII. First causes in physics

There aren't any. But what about final causes? I hear you cry. None: these are the same as first causes.

Slereah

I can't guarantee that all of Streater's point are 100% valid, but on the other hand it is a very fun book

The angriest physics book

You can tell Streater had too many conversations with @vzn or the appropriate equivalent

Yuvraj Singh...

@ACuriousMind If we can observe "gauge-dependent" things, then whatever that "gauge" transformation is, it's not a gauge transformation because those leave all observables invariant!

ACuriousMind

@YuvrajSingh... I have no idea what you're talking about or what I have to do with it

John Rennie

@YuvrajSingh... by definition we cannot observe "gauge-dependent" things because the choice of gauge is just a mathematical trick and cannot affect the real world.

bolbteppa

09:21

"I think that the problem is much simpler: cosmologists have failed to note the distinction between a gauge group and a mere symmetry group"

Slereah

That's because "gauge group" rarely has a stabdard definition

Although I guess he means bundle automorphisms leaving the action invariant v. the principal bundle group

bolbteppa

I think it's safe to say that gravity gauge business is hard

Slereah

I'm still not 100% sure of the link between diffeomorphisms and the Poincaré gauge :p

I have a smattering of theorems about it, but it's hard to get a clear picture

bolbteppa

09:39

Gauge Theories of Gravitation, Lecture 1 Part 1

►

"Reference Book: Gauge Theories of Gravitation: A Reader with Commentaries, M. Blagojević and F. W. Hehl, editors. Foreword by: T. W. B. Kibble, FRS (Imperial College Press, London 2013)
Lecture 1 & 2: Chapter 1 - From Special to General Relativity Theory
Lecture 3 & 4: Chapter 2 - Analyzing General Relativity Theory
Lecture 5 & 6: Chapter 3 - A Fresh Start by Yang-Mills and Utiyama
Lecture 7 & 8: Chapter 4 - Einstein-Cartan(-Sciama-Kibble) Theory as Viable Gravitational Theory
Lecture 9 & 10: Chapter 5 - General Structure of Poincaré Gauge Theory (Including Quadratic Lagrangians)

Going to have to go through this stuff I guess

Slereah

10:03

Hey it's Hehl

Is he the Hehl-Datta guy

How come the image is so crisp but the sound is so bad

bolbteppa

10:19

It's clearer with headphones

Gauge Theories of Gravitation, Lecture 6 Part 2

►

This one is super useful already

Pointing out the issues in Utiyama's approach

bolbteppa

10:34

Anatoly Logunov

Anatoly Alekseyevich Logunov (Russian: Анатолий Алексеевич Логунов, December 30, 1926 – March 1, 2015) was a Soviet and Russian theoretical physicist, academician of the USSR Academy of Sciences and Russian Academy of Sciences. He was awarded the Bogolyubov Prize in 1996. == Biography == Anatoly Logunov was born in Obsharovka village, now in Privolzhsky District, Samara Oblast, Russia. In 1951 he graduated from Moscow University where he studied theoretical physics. From 1954 to 1956 he worked in Moscow University, later worked at Joint Institute for Nuclear Research (Dubna). He became doktor nauk...

What about this approach to GR

"This approach permits constructing, in a unique and unambiguous manner, the theory of gravitational field as a gauge theory"

Slereah

11:14

let's see how the n cat defines solitons

aw, they don't have a fancy definition

Slereah

11:29

I'm a bit disappointed that ncatlab doesn't have a mascot called the N cat

Slereah

12:15

I wonder if the easiest way to show that the circle and square are homeomorphic is to switch from the $\ell_2$ norm to the $\ell_1$ norm

Some homotopy of $\ell_{1 + \lambda}$

Tachyon209

hi

Can I request someone to answer my question here? It' pretty simple but isn't catching enough attention.

Yuvraj Singh...

12:52

@Tachyon209 just post the question interested people will look upon it!

Tachyon209

13:10

Thanks.

ACuriousMind

6 hours ago, by ACuriousMind

@dumbasarock Please don't post links to your questions here directly after you've posted them; if everyone did that the chat would consist of little else.

Your question is an hour old, just have a little patience - many questions aren't answered after that little time.

Slereah

You know I wish people reprinted old books once in a while

With modern notation

Steenrod's not bad, but the notation is a bit old timey, and the pagesetting is bad

ACuriousMind

that would be nice

Slereah

it could use some room to breathe

Unfortunately any book old enough to be out of copyright is probably not interesting enough to warrant such a project

Although I guess I could do it for that proof of the Matthieu equation from the 19th centuyr

Tachyon209

13:32

Aah. Sorry @ACuriousMind. I'll keep that in mind. It's just that I was not getting any responses on any of my questions recently. So, was just a little skeptical.

dumb as a rock

14:30

@ZeroTheHero good evening can you take a look at a question I asked 7 hours ago but I haven't got any response on it yet. It acted like a speed breaker to my study. I could've posted link to it here but pasting question links aren't allowed.

ZeroTheHero

@Slereah I once attended (many years ago) a cosmology seminar on inflation and negative pressures at the start of the inflationary period. Present (but not speaking) was an astronomer to the Vatican Observatory. At the end of the talk this person commented something like: “ Negative pressures, curled up dimensions... really? I think my explanation is simpler.”

Slereah

I'm not sure Genesis explains the modes of the CMB

ACuriousMind

@dumbasarock Look, the idea is not to annoy people here with requests to look at a recent questions they already would have seen if they were interested in answering questions and looking at the main site. Whether you post the link or not isn't really the point.

Also, please don't ping specific people unless you have reason to believe your question is of particular interest to them.

dumb as a rock

okay

ZeroTheHero

This site is good, real good!. There are gems of questions and equally fantastic answers at all levels. I hope the good stuff doesn’t get diluted by the banal homework-style question.

dumb as a rock

14:43

I am sorry that I ping you and asked a stupid question.

Slereah

@ACuriousMind If there's a non-trivial principal bundle, does the field have a zero section?

On one hand, there's instantons all over the damn place, on the other hand, every vector bundle has a zero section

Although I guess the zero section of $TP$ may not be the same as the zero section of $TM$

ACuriousMind

@Slereah What field?

It's bundles that have zero sections, not fields

And the principal bundle doesn't have a zero section because it has no notion of "zero" :P

Slereah

The corresponding field of the connection :p

I guess in $HP$

ACuriousMind

what is true is that no non-trivial principal bundle admits a global section.

ZeroTheHero

@dumbasarock Your question is not stupid but it’s not clear and I don’t have time to deal with this right now.

ACuriousMind

14:57

The connection form is a $\mathfrak{g}$-valued one-form on $P$, of course it can be identically zero.

the trick for a non-trivial bundle is that the connection form only descends to a connection form on the base spacetime in a trivialization, so you don't get a global connection form on spacetime for non-trivial bundles

This is because the non-trivial principal bundle does not admit a global section by which you could pull back the connection on $P$ to get one on $M$

Slereah

ah, I guess the instanton business happens on the overlap maps?

if you try to have a zero section

ACuriousMind

Yes, the transition functions determine the (non-)triviality of the bundle and hence the instanton number

Slereah

I think Naber talks about that

I need to get back in that

ACuriousMind

This is how you get things like $\pi_3(G)$ classifying bundles over $S^4$, because on an $S^4$ the overlap of two trivializations is homotopic to $S^3$, so choosing a transition function is the same as picking an element $\pi_3(G)$.

Charlie

Do spin-2 particles collectively have a name like fermions, scalar/vector bosons etc.?

Slereah

15:08

They are called tensor fields, usually

Due to reasons, there are typically no tensor fields of rank higher than 2

ACuriousMind

The name is "graviton", theories with spin-2 bosons that are not gravitational are usually inconsistent

Charlie

Is that in the context of qft? So is it excluding say the riemann curvature tensor field

I don't know any qft so this is a super soft question I just wondered if they had a fancy name

Slereah

I mean having a spin-2 particle is usually a QFT idea in general

@Charlie $(1,1)$ irreps of the Lorentz group?

ACuriousMind

@Charlie What except QFT would be used to talk about "spin x bosons" anyway?

Charlie

I only mentioned the curvature tensor because you mentioned rank 2 tensors

Slereah

15:11

Well as mentionned, typically only gravitons are spin 2

So the tensor fields are usually $\approx$ the metric tensor

Charlie

I'm already out of my depth, thank you though

:)

Slereah

Spin business is usually nasty

user434058

@ZeroTheHero Hi! I am only acquainted with electric and magnetic flux and that's the reason why I have only used them in my tag wiki edit. Please do edit the tag wiki to make the tag more general. Thank you! :)

user434058

physics.stackexchange.com/review/suggested-edits/297952

ACuriousMind

Tag Wikis are only really useful if they contain information not obvious from the tag name itself.

"Use flux for questions about flux" is not very useful

Slereah

15:21

You never know

Maybe a caveman might get some use out of it

Yuvraj Singh...

Stop***

ACuriousMind

@Slereah A caveman that can read English? :P

@YuvrajSingh... What?

Yuvraj Singh...

Tried to change the topic , please continue

ACuriousMind

How is "stop" followed by three asterisks supposed to change the topic? If you offered an alternative topic in a comprehensible manner - or gave reasons to stop discussing the current one - you might be more successful.

Charlie

15:38

CuriousMind you probably have been asked this a million times but who's in your profile picture?

Yuvraj Singh...

@Charlie he had replied it several times:-)

ACuriousMind

Jan 18 at 19:14, by ACuriousMind

3 hours ago, by ACuriousMind

22 hours ago, by ACuriousMind

@Knight It's the protagonist of Disco Elysium

Yuvraj Singh...

@ACuriousMind there you go I have one question!

how the field theory corresponds to black holes in the gravity dual?

Charlie

I see haha

Slereah

His name is hobocop

Yuvraj Singh...

15:42

@Charlie haha?

I consider string theory as stupid theory with no predictions, and no one can test it's existence and we study it with all the rigorous mathematics!

ACuriousMind

@Slereah Only if you choose so!

Slereah

There is no freedom of choice

All is determined

Slereah

16:08

$$ \array{ && \longleftarrow \\ & \swarrow && \nwarrow \\ V && && V^\ast \\ {}^{{\exp(\tfrac{i}{\hbar} H t)}}\downarrow && && \uparrow^{{id}} \\ V && && V^\ast \\ & \searrow && \nearrow \\ && \longrightarrow } $$

@ACuriousMind Please explain

ACuriousMind

It would appear you've botched some MathJax :P

Slereah

Category theory is hard in mathjax

ncat has some weird definition in their mathjax

ACuriousMind

It's probably better if you just link to the page you're wondering about

Slereah

I'm afraid I was somehow jesting

I don't expect you to explain all the FQFT article

ACuriousMind

I'm afraid category theory parody may be even harder to understand than category theory ;)

Slereah

16:11

Oh that is 100% a real diagram

Despite being a loopdeeloop

ncatlab.org/nlab/show/…

it is here, if you are curious

bolbteppa

16:42

That's supposed to be Penrose notation for the partition function...

Slereah

18:04

Spellcheck has been great, but whoever figures out how to get grammar check to work is guaranteed a Nobel.

2

Pole_Star

18:45

I have been doing some sums on this kind of problems

But really cant figure this out

Slereah

18:59

Use the Poisson equation

Pole_Star

Yeah but stuck at the laplacian part

Slereah

What has you down

Physics Meta

21:00

0

Q: Where does scoring from question and answers come?

I see that some of my questions and answers have positive and negative integer score. Where does it come this score? I am new in the forum.

vzn

22:25

@Slereah lol asking for trouble, as usual? and ryan is long nowhere to be found? if you like science comics why dont you try sidney harris, he understands kuhnian paradigm shifts (unlike many "scientists") :P sciencecartoonsplus.com/pages/gallery.php sciencecartoonsplus.com/gallery/physics/index.php

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