The h Bar

Slereah

12:20 AM

Hm

Is higher gauge field theory done with a connection that defines holonomies of higher dimension than 1?

So it defines a "geodesic" for a $p$-brane

John T.

4:18 AM

How do you guys like to stay updated on new math/physics papers

Do you just straight up read papers from journals or do you have some sort of news outlet/forum that you use?

antimony

4:36 AM

i personally like phys.org

phys.org

Obliv

5:55 AM

Thanks! I'll check it out @antimony

BannedUser

8:46 AM

PV/nT=R=const.
Do all of these variables change as the balloon is heated?

Temperature T increases with heating.
Air molecules can escape through vents in the fabric, so n can vary.
However, V and P are constant. Once the balloon is inflated, its volume V is constant. Hot air balloons are open at the bottom, so the pressure P inside the balloon is equal to atmospheric pressure outside.

I don't think pressure will be fixed if balloon in heated

Samyak Marathe

9:11 AM

Greetings

If anyone could help me in this question: physics.stackexchange.com/q/671392/274910

Slereah

9:36 AM

Reading nlab's supposedly pedagogical introduction to stacks

"To pick just one example: there is a topological space that goes by the name $K(Z,2)$ or $BU(1)$ and is called an Eilenberg-Mac Lane space."

This is the introduction

I don't know what an Eilenberg Maclane space is nlab

bolbteppa

@Slereah Ple... googles what it is ... b... doesn't understand what it is...

Nihar Karve

it's just a CW complex with only one non-trivial homotopy group

ACuriousMind

@Slereah then why are you trying to learn about stacks :P

Slereah

@ACuriousMind Well they keep going on about it

Apparently higher gauge theories are stacks

and it's very important

I sort of know what $BU(1)$ is but barely

ACuriousMind

sure, but I don't think an E-ML space is an outlandish example for an advanced topic in algebraic topology/geometry

It's like you're complaining about an analysis text using a sin function as an example but you don't know trigometry :P

Slereah

9:51 AM

I guess I must go back to algebraic topology

Sigh

What's a good algebraic topology book that goes a little further than the one I was reading previously

It was all CW complexes and de rham cohomologies and whatnot

ACuriousMind

did you go through Hatcher? It's the usual recommendation.

Slereah

I think that was the one yes

I don't think it talked of the EML space, or at least I can't remember it

Although...

I don't think it was Hatcher

I think it was some physicist oriented book

bolbteppa

theoreticalatlas.wordpress.com/2014/08/15/…

That makes some interesting points

"The starting point, though, is that the defining features of stacks capture two crucial principles from physics: the gauge principle, and locality.

The gauge principle means that we need to keep track not just of connections, but gauge transformations, which form respectively the objects and morphisms of a groupoid.

“Locality” means that these groupoids of configurations of a physical field on spacetime is determined by its local configuration on regions as small as you like..."

Then it seems to say a field theory is map (functor $F$) from a manifold $\Sigma$ to a (moduli) space of fields on $\Sigma$, $F(\Sigma)$, then it calls this a pre-stack, and says a stack is this with some extra condition that amounts to locality.

Show me how basic E&M is a stack nlab

Nihar Karve

10:07 AM

well the EM field is a cocycle in differential cohomology with coefficients in the stackification of the groupoid of forms apparently

Slereah

it probably is

"It follows therefore from these three tests, that the repulsive force that the two balls — that were electrified with the same kind of electricity — exert on each other, follows the inverse proportion of the square of the distance."

Things were a bit simpler in Coulomb's time

bolbteppa

But these simple ideas were also commonly written in unreadable Latin then too

Slereah

books.google.fr/…

Apparently not

It's a bit old timey but I can read it

1785

Hope you didn't lose your head Mr. Coulomb

bolbteppa

What's a higher gauge theory, a 2 form etc?

Slereah

Apparently he got along with the new government

Good for him

@bolbteppa Apparently so yeah

Instead of defining what a geodesic is, higher gauge theories define what a geodesic $p$-brane is, basically

So it will define the path of a $p$-brane, and therefore be defined by some $p$-rank tensor

bolbteppa

10:16 AM

By geodesic you mean a point particle coupled to the EM field follows a path which is a geodesic of something even in Minkowski space

Slereah

Point particles get a 1-forms, strings get a 2-form, etc

@bolbteppa Basically yes

that is the physicist way of how I understand it to be

Except $p$-gauge theory is much much worse

I'm guessing that for a lot of it there's a natural extension of the 1-gauge to the 2-gauge

There's a natural way for strings to propagate through curved spacetime for instance

but I think some of them are brand new animals

Like whatever the RR-connection is

bolbteppa

ncatlab.org/nlab/show/higher+gauge+field

Slereah

ncatlab.org/nlab/show/RR+field

Ramond-Ramond

The field so nice they named it twice

Maybe I should work out what the Levi-Civita connection is for strings

That may be a good point to start

It's probably something that flows naturally from the usual one

bolbteppa

Giving them the benefit of the doubt, the fact that these higher $p$-form gauge fields can themselves transform under $p-1$ forms etc leads to a structure that needs to be given a name

Slereah

is it

the stack

or an example of one at least

"A connection on a bundle gerbe is a slight variant of a Cech-realization of a degree 3 Deligne cohomology cocycle."

That explains it I guess

ncatlab.org/nlab/show/…

Possibly whatever this is

bolbteppa

10:32 AM

I've heard that the number three is a specific value of Grothendieck B-functor on the space of cardinalities of permutations of Cech cycles of flux boundaries of finite rank

Writing $A_{\mu} dx^{\mu}$ in this context is probably more offensive than not knowing what an EML space is

Slereah

I think the B field is supposed to be the connection in this general case?

It's not a specific field

Although maybe not, it seems specifically the U(1) case

Does gravity not count as a gauge field in string theory?

By which I mean the curvature of the target manifold

bolbteppa

10:49 AM

ncatlab.org/nlab/show/circle+n-bundle+with+connection

That's supposed to be for $n$-forms you get an $n$-bundle with connection...

Slereah

Isn't the circle n bundle just fancier versions of EM though

Slereah

11:01 AM

I mean the Polyakov action on a curved spacetime already depends on the Levi Civita connection, isn't that already a higher gauge

Connection acting on a string

bolbteppa

I'd say it's supposed to go the same way

Slereah

Why can't string theory be simple

bolbteppa

The point is, a simple idea leads to $\infty$ gerbes pretty quick but you can just ignore all that

It's like focusing on limits because it involves calculus in a sense, obviously it's important and a whole field of math but still

Slereah

Idk I figured it might make things simpler since I already know Polyakov

also does Polyakov depend on the connection

bolbteppa

Yeah if I could just see a straightforward explanation of all this I'd give it a try

Slereah

11:11 AM

It depends on the metric, and the EoM depends on the connection

bolbteppa

But the only real selling point is a promise of a broader perspective on the tools involved, so at the very least it should be explained simply

Slereah

Ah well

U(1) isn't too complicated either I guess

Slereah

12:59 PM

Hm

I guess if the connection isn't metric or torsion free

The string action doesn't change, does it

although... In the point particle limit, it should nudge for non-metricity

but IIRC the action for particles in that case is complicated

and it's not the Polyakov action

bolbteppa

1:52 PM

Barbashov has loads of connections in these actions around the middle/end

Semiclassical

o/

bolbteppa

New Shepard Mission NS-18 Webcast

►

Don't judge me for supporting space joyrides

Semiclassical

a quantum question that's in my brain today. suppose i start with some pure separable two-qubit state, i.e., $\rho = |\phi\psi\rangle\langle \phi\psi|$

and then i apply a random unitary to both qubits to get $(U\otimes U) \rho (U\otimes U)^\dagger$, and average this over the sphere to get $\rho_{avg}=\int (U\otimes U) \rho (U\otimes U)^\dagger d\mu(U)$

Will $\rho_{avg}$ be a separable mixed state?

ACuriousMind

that's essentially asking "does the integral commute with the tensor product", right?

because with $\rho = \rho_1 \otimes \rho_2$ you're asking if $\int (U\rho_1U^\dagger) \otimes (U\rho_2U^\dagger)\mathrm{d}\mu(U) = \left(\int U\rho_1 U^\dagger\mathrm{d}\mu(U)\right)\otimes \left(\int U\rho_2U^\dagger\mathrm{d}\mu(U)\right)$

or would you expect it to be separable but not equal to my r.h.s.?

Semiclassical

2:13 PM

well, $\rho=\rho_1\otimes \rho_2$ means the state is simply separable

the definition i'm seeing for 'separable' is $\rho=\sum_j p_{j}\, \rho^A_j\otimes \rho^B_j$ with $\rho^A_j,\rho_k^B$ being states

(if you drop the requirement that $\rho_j^A,\rho_j^B$ be states, every $\rho$ is of this form)

i did test by the P-H criterion, and i don't seem to run into negative eigenvalues of the partial transpose for any initial choice of $\rho$

BannedUser

hello when is pressure of hot air balloon smae as atmospheric pressure?

Semiclassical

that's not sufficient, of course, but it's something

BannedUser

I think when it is not inflated

Semiclassical

@BannedUser suppose you have an inflated balloon. what would happen if the pressure on its outer surface was larger than on its inner surface?

BannedUser

my book says that the pressure inside balloon is same as atmospheric pressure when balloon is heated

@Semiclassical balloon becomes smol

Semiclassical

2:25 PM

right. so if the balloon's size isn't changing, then the pressures have to be equal

BannedUser

so book is wrong right?

Semiclassical

probably depends on what we mean by heated

what process

if you heat slowly, though, i'd anticipate that the balloon remains in equilibrium the whole way

so the net force on the balloon remaining zero, hence same pressure inside as outside

ergo constant pressure

BannedUser

you mean heat slowly so it will cool fast?

book says rising temperature

MicroservicesOnDDD

3:09 PM

I asked a very creatively phyics question (actually, it was not a question at first, just a funny story.) How do I keep this as a question here? Sometimes you have to bend the rules, and having one funny story might cause a bad precedent, so even though I want my question to stand, perhaps it should not. What do you think? physics.stackexchange.com/q/671441/284011

Slereah

nlab doesn't have much to say on LQG : ncatlab.org/nlab/show/spin+network

ACuriousMind

3:28 PM

@MicroservicesOnDDD 1. Unless you ask a bunch of off-topic questions and then get hit by the automated question ban, it doesn't really matter whether some of your questions are closed or not - and actually deleting the question makes the automated blocker consider it an even worse question. 2. There isn't really a way to make your question on-topic - we just don't do ancedotes or jokes as the focus of a question on the main site

bolbteppa

3:53 PM

Shatner's speech after landing is incredible

Nihar Karve

4:04 PM

@Slereah the amount of description is commensurate with the validity of the theory of course ;)

cOnnectOrTR 12

5:10 PM

Can somebody answer this:

In v^2=u^2+2as it is the s displacement travelled by the body during its acceleration a and the change of its velocity from u to v

u and x0 is the speed and initial position at t=0

v and x is the speed and final position at t=t

Please verify!

Slereah

"Spin foam models are particular models aimed at finding a theory of quantum gravity. Their relation to Einstein-Hilbert gravity in classical limit seems however not to be convincingly argued for in the literature."

Snap

are the nlab people staunchly against LQG

bolbteppa

Some strong comments here too

> 'Still another suggestion has been that ordinary quantum field theory might be seen to apply to the ordinary configuration space and action functional of general relativity, if only a suitably adapted parameterization of the configuration space is chosen. Notably one observes that Riemannian manifolds may be encoded in terms of connections on the tangent bundle – the Levi-Civita connection – this being manifestly analogous to the nature of the fields in Yang-Mills theory. (See first-order formulation of gravity).

> However, little progress has been made in understanding the configuration space of smooth connections in terms of loop observables. In most of the LQG-literature instead it is assumed from the outset that it makes sense to pass to generalized connections ... It is is not clear how this configuration space relates to that of ordinary gravity... The problem with discriminating between all these proposals is the combination of two problems.'

cOnnectOrTR 12

@JohnRennie @ACuriousMind @Semiclassical ?

bolbteppa

What does that mean: '...if only a suitably adapted parameterization of the configuration space is chosen. Notably one observes that Riemannian manifolds may be encoded in terms of connections on the tangent bundle'

Slereah

6:16 PM

why are there so many branes

PM 2Ring

7:33 PM

This may be of interest: a Firefox add-on that speeds up MathJax & jQuery. math.meta.stackexchange.com/q/34170/207316

@Slereah Allen Hatcher is a rather good writer, IMHO. I started reading an earlier draft of his Topology of Numbers a year ago. I managed to get about 3/4 of the way through before I decided it was too hard for me. ;)

Semiclassical

9:06 PM

@cOnnectOrTR12 the way I like to organize this is to solve for acceleration: a = 1/2 * (v2^2-v1^2)/(x2-x1)

For velocity and position at times t1 and t2

It does assume constant acceleration of course

geocalc33

9:35 PM

any idea how to construct a flow that sends points (x,y,z) in (0,1)^3 from (1,0,0) to (0,1,1) s.t. the flow is bounded by [0,1]^3

it's a generalization of a flow that sends (x,y) \in (0,1)^2 from (1,0) to (0,1) s.t. the flow is bounded by [0,1]^2

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