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In bosonic string theory, the critical dimension arises as a consequence of Lorentz covariance in light-cone gauge and alternatively as prevention of Weyl anomaly via CFT approach. Does the Weyl anomaly have some "deep" connections with Lorentz covariance?

I see the same thing when evaluating the normal ordering constant a=1. It was derived as Lorentz invariance in light-cone gauge and alternatively as a consequence of maintaining Weyl invariance of the vertex operators.

So what's the deal with Weyl and Lorentz symmetries? They should be unrelated because they are separate symmetries of the Polyakov action, right? but somehow something feels to connect them...

Well the Weyl group is just the Lorentz group with dilations

And Weyl transformations leave the light cone invariant

Not sure if that helps

ProphetX going hard with that answer

Usually when you compile a latex file, it goes right to where you made the last edit, but sometimes (if the file gets huge) it starts showing the next page or something, any idea why and/or how to stop that

what do you mean by "it goes right to"?

do you mean that whatever editor you're using opens the pdf after compiling and jumps to the location of the edit in the pdf?

Isn't that a function of the development environment you're using rather than Latex itself?

Yeah

what John says, you need to find people using the same editor :P

what are you using?

You edit a word say and the pdf then centers around that word

texmaker

haven't used that for years, no idea whether you can stop it from doing that

Ah, the only GUI I've used is MikTex so I have no experience of Texmaker. Sorry :-(

(I generally use TexLive and the command prompt)

No worries, just very annoying

@ACuriousMind this might be a long conversation. Would you like to talk here?

@MoreAnonymous if you need a long conversation to explain your question to me, then your question is unclear.

I'm not so much interested in understanding your question as I am in you asking self-contained questions.

@ACuriousMind I suspect (perhaps wrongly) you are coming with some assumptions which I dispute such as "The equivalence principle is a feature of general relativity"

@ACuriousMind I do think it's self contained though

"The equivalence principle" is a vague term that can mean a dozen different things

@ACuriousMind I quote the one I'm referring to

they all mean "gravity is indistinguishable from acceleration"!

the devil is in the detail of how you formalize that!

Hence the word locally

And its not obvious to me how to talk about any notion of locality without position

@MoreAnonymous I really don't think so, especially because your actual question at the end talks about a "coordinate transformation" and a "metric" but nothing in the motivation part mentions coordinate transformations or metrics

@MoreAnonymous that's not a reason to pretend there's a position operator when there's isn't!

@ACuriousMind Are you saying the notion of first quantization fails while approaching the surface of a blackhole>

?

Even writing the Hamiltonian you wrote is a gigantic leap, let alone this $[a,r] = 0$ claim, how can one talk about the equivalence principle by comparing the path of a free particle in an inertial frame in a potential to the path of a free particle in a non-inertial frame if we can't even measure how it moves

e.g. standard QFT has a notion that locality means that fields commute when their arguments are at spacelike seperation

@MoreAnonymous yes, I'm saying trying to do canonical quantization near a black hole is a silly idea

(and also - your question doesn't make any assumptions specific to "near a black hole", another context clue that seems to be contained in your mind but not in your question)

@ACuriousMind Ugh I'll delete for the time being

@ACuriousMind A lot of people assume it when say modelling the radiation that comes out while the gas gets squashed around a blakchile

*blackhole

@MoreAnonymous See, if you have a specific thing you're referring to here ("Paper X does Y, can I apply this in context Z?") that should be part of your question

People who read your question don't have any of the context you have, in particular while they might theoretically know papers you've read they might not make immediate connections between them and what you're writing

@ACuriousMind Okay then the size will expand exponentially. But sure I'll do that

when the question balloons like that you should consider whether you can ask a smaller part of it as an individual question

@ACuriousMind I'll sound like a crank if I say something like why does modelling the blackhole image make sense?

Though I might sound like one either way

:P

Would this be entertained though^

you sound like nothing to me because I don't know what "modelling the blackhole image" means

People tried to reproduce this image on their computers

And the paper I read seemed to indicate you can use first quantization

(which I'm searching for right now)

Okay, so the first step would be to a) read the paper more than once and then b) ask specific questions about steps that seem unclear to you

while your approach seems to have been to take a vague idea of what the paper does and run with it in a random direction, then ask a question without reference to the paper so it has become impossible for anyone to tell apart what might be an error in the paper itself, a mistake in your understanding of it or an error in your application of it

can you see how that's difficult for anyone to follow that doesn't know you've read that paper?

@ACuriousMind ummm .. yea my bad

Can someone give me a reference(preferably a book or review paper) of Anomalies from a geometrical viewpoint?

One which views anomaly as an obstruction of representations of the symmetry group on the Hilbert space...

@ManasDogra have a look at Bertlmann's Anomalies in Quantum Field Theory

Glossed over the book a bit, not sure if it doesn't contain what I expected but I was actually referring to an answer by you here.

@ManasDogra i dont see a link :(

@MoreAnonymous Sorry I pasted something else

@ManasDogra no worries

@MoreAnonymous If it isn't too much to ask, are you from West Bengal?

Why?

I actually saw a reply by you to Balarka Sen of you staying in Sodepur for some months so I thought that you are from there...and I am from West Bengal that's why

@ManasDogra I don't remember this conversation

@ManasDogra But I hope you have a good physics career

@MoreAnonymous I just noticed now! It's someone different...his username also had the phrase anonymous, so i confused

@ManasDogra Hahaha lol

@MoreAnonymous Yeah Thanks...

I think I only once happened to enter a conversation with Balarka

it was ages ago

Something like that

Interesting...

@ManasDogra I'm guessing your doing post graduate? But your QFT knowledge is probably better than mine :)

I am actually in UG 2nd year, and it seems so...it maybe isn't :)

@ACuriousMind So as I was saying...I don't know for sure but does it contain stuff related to your answer and the answer by David Bar Moshe you were referring to in that answer?

Dang first Nihar now you. I like the "intellectual" monsters this community is fostering :D

@ManasDogra Ah, I only answered to your first request: The geometric approach to anomalies is not really the same as the "anomalies are group extensions" approach

Bertlmann is about the geometric approach, I don't recall off-hand if and how much extensions feature there

David Bar Moshe has a bunch of references to the group extension interpretation here

(it involves gerbes! :P)

@ManasDogra Weyl invariance classically ensures that the energy-momentum tensor is traceless, however this tensor is quadratic in the fields so there are normal ordering ambiguities on quantization, thus the trace may be non-zero on a quantum level. Similarly the Lorentz generators are quadratic in the fields and so may pick up normal ordering ambiguities, especially in a coordinate system like lightcone coordinates where (due to the constraint) one finds cubic terms in the oscillator expansions.

Maybe this is the similarity/connection you are noticing

@ACuriousMind Ah yes ... this was it

the Schrödinger-Newton equation was created in 1969

Pretty late

That's later than a bunch of quantum gravity theories

Powerful log scale

Fit the whole long line in there

Consider two irreps of a group. The tensor product of these two irreps can be written as a sum of irreps of this group. In this sense, the product of these irreps seems to be closed in some sense. Is this directly related to the fact that the group is closed under group operations?

@B.Brekke This is not true for all groups; there are groups whose representations are not always completely reducible, so there is no guarantee the tensor rep is a sum of irreps

so it is not a simple consequence of the group operation being closed - having completely reducible reps is an additional property a group may or may not possess

My professor (assuming he wasn't quoting anyone) said: "Einstein asked the right questions and gave wrong answers. Bohr asked wrong questions and gave the right answers"