The h Bar

1:02 PM

@Koolman Aha. Nowhere in the link does it say your answer doesn't match (or, well, it's information buried in the comments). Also you already have an answer that says that your result is correct and the "given" answer wrong. Again, what's your question?

Koolman

@ACuriousMind I just want to confirm it one more time . May be Sammy and I have missed something .

ACuriousMind

@Koolman See, would it have been so difficult to say that from the start instead of just pasting the link in here? If you want people to help you, you should make it clear to them what you actually want.

anonymous

@Koolman 40 is the right answer. I am sure

Sammy's answer is correct

and yours too

Koolman

@ACuriousMind Sorry , it will not happen again

@anonymous thank you

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

1:27 PM

You should try to be a bit more polite my friend :-)

Koolman

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ can you please tell me in which way do you think I am aggressive

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ i don't want to be rude or aggresive

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

I know it's tough when the book makes a mistake in the answer.

Koolman

Yeah

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Is this a well known textbook?

Koolman

No

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

1:32 PM

There you go.

Slereah

@ACuriousMind what the hell is functorial quantum field theory

Koolman

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ ??

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Well known textbooks have less typos.

None of them are perfect.

Koolman

Yes , but few times I got the answer which does not match . But later I get to know I have made a conceptual mistake

For this book

Secret

ncatlabs have a lot of info about FQFT, which I currently don't have the background to understand as my category theory is preliminary

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

1:37 PM

Use a back up textbook @Koolman

ACuriousMind

@Slereah Viewing QFT as a functor from cobordisms to vector spaces. Basically, you think of a "spacetime" (such as a cylinder, a pair of pants, or some other manifold with boundary that you get when you "cut off" a spacetime at times $-T$ and $T$) as a morphism between the past and the future boundaries. The FQFT assigns a Hilbert space to each time slice and a partition function/propagator to the morphism.

Koolman

I would find it

Hammar

can I ask questions here ?

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Ask away.

Slereah

is that assuming a spacelike hypersurface for the cutoff?

ACuriousMind

1:39 PM

@Slereah I think we usually formulate those FQFTs in the Euclidean setting so we don't have to worry about that ;)

Slereah

I think "euclidian setting" sounds like a lot of worries to me!

At least if you do it in curved space

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Have you looked in the library @Koolman?

ACuriousMind

Well, since I haven't really seen anyone use the FQFT framework for something other than TQFTs, it doesn't really matter to begin with...

(I haven't particularly followed the FQFT developments though)

Slereah

Alrighty then

Better stick with AQFT then

Koolman

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ yeah I have one more book whose solution is uploaded

But I have almost completed it

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

1:42 PM

Try a real library.

Koolman

It is far away from my home

ACuriousMind

I mean, cobordisms are usually a topological construction. Having to care about them being endowed with metrics sounds a bit annoying to me - usually you declare homotopic cobordisms to be equivalent, and I fear that viewing them as Riemanniam manifolds destroys some nice properties. I'm just rambling, though

Koolman

If I got time , I will definitely visit there

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Good luck.

:-)

Slereah

There are cobordism in GR!

Secret

1:46 PM

0

Q: Why the negative thermal expansion of polymer deserves a nature paper?

A Normal Experiment: If you take a piece of the rubber band, and use it to hang a weight and then gently heat the rubber band. Finally, you will see that the weight will be lifted up! This is the negative thermal expansion of polymers. This effect can be explained by statistical mechanics (chain...

...because the effect is large? or because it is drug related?

Slereah

one thing that bothers me a bit about QFT "axiomatizations" is that a lot of them are just bare minimum conditions for a theory to be a QFT

And they don't really bother with dynamics and such

Balarka Sen

@ACuriousMind Not declaring homotopy equivalent rel boundary cobordisms to be equivalent is where Lurie's whole $\infty$-theory arises from. Instead you declare cobordant cobordisms (those are manifolds with corners) to be 2-morphisms, and cobordant cobordisms between cobordisms to be 3-morphisms and so on and so on

I didn't know people actually studies cobordisms in the Riemannian category

ACuriousMind

@BalarkaSen Ah, that's what "extended TQFTs" are.

Balarka Sen

Right

ACuriousMind

Still a TQFT though, no metrics in sight

Balarka Sen

1:48 PM

Why do you think cobordisms with metrics are a bad thing to study? I don't know, so just askin'

ACuriousMind

@Slereah Well, it's hard enough to show that "minimum" for the "actual QFTs" we have!

heather

hello.

ACuriousMind

How would you know what axioms to impose on the dynamics if you don't have anything to model them after?

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Hi.

Slereah

@ACuriousMind I get the feeling that a lot of those axiom systems are also for QFTs we don't have

Like can't we at least define the CCR and the Hamiltonian

I know some theories don't have them, but you know

it would be nice

most theories do

heather

1:53 PM

Michelle or Melania? <- just to make sure, is this referencing Mrs. Obama and Mrs. Trump (asking which is better)?

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Michelle.

heather

lol. I don't think that's a fair question - Mrs. Obama was in office for 8 years; Mrs. Trump for two weeks.

ACuriousMind

@BalarkaSen Not "bad" as such, just not as nicely behaved. The problem with formalizing non-topological QFTs as FQFTs is, I think, that we can't actually write down the functor since the path integral is ill-defined.

@Slereah What do the CCR matter? I think one lesson from Haag's theorem is that the CCR are not all that fundamental as they are in QM

heather

David Z or Ron Maimon? - I have a feeling this one has some significant history I don't know.

ACuriousMind

And since you're always going on about curved spaces and whatnot, "the Hamiltonian" is also an ill-defined or at least non-covariant notion.

Slereah

1:57 PM

Not being covariant isn't much of a problem

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

@heather is this a word game?

Slereah

In the end you still have to define it except implicitely anyway

heather

0

A: February 20th Ask Me Anything with heather: Question Pool

Einstein or Bohr? Harvard or MIT? Michelle or Melania? Tesla or Edison? Ubuntu or Fedora? Heisenberg or Schrödinger? Dems or Repubs? Strings or loops? Socialism or Capitalism? Frequency or time? Trump or Hitler? David Z or Ron Maimon?

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ ^

Slereah

The constructions of free scalar fields are always those big list of field properties that are just exactly that

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

I see @heather :-)

ACuriousMind

1:58 PM

@heather lol, I'd advise you to not answer those questions unless you want to start several holy wars at once :P

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

^

heather

at least no one's done "vim or emacs?" yet.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Unholy wars too :P

heather

@ACuriousMind oh, I'm definitely not answering some of them.

Slereah

the worst part is probably the property of the propagator

heather

2:00 PM

I'm not answering Kenshin's question.

Slereah

Among the list of properties is $[\phi(x), \phi(y)] = D(x,y)$

As a fundamental property that seems odd

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Good idea.

Fawad

@heather @heather trump or Hitler, lol

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

:O

heather

I mean, Hitler's clearly worse than Trump. I hate questions like that - we have to be reasonable about the situation at some point =P

ACuriousMind

2:02 PM

@Slereah Personally, I've come to think that the immense difficulty we have in formalizing QFT is that it really isn't a fundamental theory, just an impressingly efficient effective one.

Slereah

@ACuriousMind True, but I also think that AQFT isn't gonna be the fundamental theory either

So I'm not sure there's a lot of use in pretending it's gonna be some general theory

Fundamental theory is gonna be some quantum gravity shenanigan

A theory so awful that no calculations will be possible

ACuriousMind

What I mean is that we're looking at some funny limit of a theory that might be axiomatizable more easily. It's not evident that trying to formalize such a limit is useful

Slereah

Only one way to find out I say

I get the feeling that people are a bit too quick to dismiss experimental aspects for quantum gravity

there's this general notion among a lot of people that it will not possible to check for a long time

I'm not sure if that's a very good attitude

The idea that we need energies around Planck to check for it is a bit naive

Since quantum gravity effects will happen in all processes

Just with varying degrees of smallness

ACuriousMind

In particular, trying to formalize it on curved space looks like an error. If we're doing effective theory anyway, we might as well view gravity as a field theory instead of trying to shoehorn the full non-perturbative aspect of gravity into the effective framework of QFT. I view any theory that treats gravity as ultimately "special" with suspicion.

Slereah

that is fine too in my opinion

ACuriousMind

2:09 PM

@Slereah Well, has anyone made a plausible low-energy prediction for any QG effect?

Slereah

Define "plausible"

ACuriousMind

In principle accessible to experiment and derived from a non-crackpot theory of QG

Slereah

Not so far as I know, no!

But I think the way forward is probably more sensitive equipment and not bigger colliders

ACuriousMind

Then that looks like a pretty good reason for people to dismiss experimental aspects so far, no?

Secret

Is it better to have a background dependent or background independent QG?

Slereah

2:11 PM

Define "better"

ACuriousMind

@Slereah Yeah, but you need predictions to know what equipment to make more sensitive :P

Slereah

I do wonder if there's any good predictions involving effects in neutron stars

I'm guessing that's probably the best place to check for such effects

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