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...
It is said in wikipedia that Minkowski spacetime isometries, i.e. the transformation that preserves
$$
(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2-(t_1-t_2)^2
$$
between points, can be represented as $\mathbb{R}^{1,3}\rtimes O(1,3)$, meaning that it consists of transformations with the form
$$
x \mapsto ...
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
@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
@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!
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)
@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
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?
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
I think I only once happened to enter a conversation with Balarka
it was ages ago
Something about a conversation between me and acuriousmind. Curious saying heat is some co-chain. Me saying I didn't see why you couldn't argue that heat should be a weight on each infinitesimal
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?
@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
@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
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"
After discussion about this was started two and a half years ago, I'm here to share that I'm enabling a test of three-vote close on Physics today. Firstly, I'd like to thank you for your patience. There's been a lot of discussion about this and I mentioned my primary concerns about making this ch...