/sci/ - Science & Math

>>11506823
Because antimatter also interact with gravity the same way as regular matter, so it wouldn't make sense for them to cluster around a specific spot in the universe while regular matter is so uniformly spread.
This discrepancy between matter and antimatter is the strong CP violation, and many HEP/cosmo people have been working on this for decades. I doubt you can just sweep it under the rug with a post on 4hcan.

>>11044479
This is actually incorrect. It's true that, from an effective point of view, there can always be a larger energy scale the physics of which decouples from that of our current theory. The way this energy hierarchy is segregated is with the spectrum of the theory. If the spectral gap for a theory grows with the RG flow, the physics at the IR fixed point for the two spectral "islands" decouple and an effective field theory, describing only the low-lying spectrum, can be constructed.
Now if the spectral gap all remain constant even at the IR fixed point, we then have absolutely no definitive energy scale at which we can make our "effective" distinction. String theory, being a CFT, is an example where this occurs; all primaries increase eigenvalues by a fixed discrete value, and all conformal descendants can do is shift the Verma modules around. This means that there is no inherent energy scale to string theory, and if it truly is an effective theory then its "parent" theory must have a spectrum [math]\cong \mathbb{Z}[/math], where one of the gaps suddenly start to increase without breaking any symmetry or lifting any degeneracy. At the very least with our current understanding, this is absurd.

>>10377522
First of all not all [math]T\in B(X)[/math] are diagonalizable. Second of all [math]T^n = (SDS^{-1})^n \neq S^n D^n S^{-n} \neq SD^nS^{-n}[/math].
>>10378184
This is related to Dirichlet principle: the solution to the Laplace equation on [math]D[/math] is the minimizer of the functional [math]I[u] = \int_D dx|\operatorname{grad}u|^2[/math]. In general one can express PDE's [math]L=0,~ L \in \mathcal{B}(X) \otimes_X \bigwedge TX[/math], linear or otherwise, as the first variation condition for a Frechet and Caratheodory functional [math]I: X\rightarrow\mathbb{R}[/math] after applying Raymond-Dubois. In cases where Raymond-Dubois doesn't hold pointwise or when [math]I[/math] isn't Caratheodory, one can only obtain saddle points of [math]I[/math] in a "weak" sense, i.e. under an integral. This leads to the theory of distributions and generalized functions.
>>10378947
Because the action of rotation [math]O\in O(3)[/math] on a translation [math]T[/math] is [math]O^{-1}TO[/math], not [math]OT[/math]. If you just rotate and don't rotate back then you don't translate to the same point in space.

>>10062546
>be giving lecture
>see a student take pic of me with flash
>mfw

I'm going to head to the gym soon so I'll just drop this here: https://arxiv.org/abs/1303.1202..
This article seems to be describing the kind of correspondence I'm interested in, although it focuses on the fusion (operator) algebra instead of the KZ connection. In certain cases (e.g. under assumptions of unitarity and metaplecticity) the two concepts are equivalent, I feel that by constructing an analogue of the KZ connection from a more general form of TQFT would allow us to look at TQFT/CFT in a more general perspective. And since the fusion algebra doesn't tell us anything about the geometry, it isn't useful when I want to look at AdS/CFT.
Overall the article feels like it is limiting itself to a class of very special UMC's so that it could make an 100% accurate and understood correspondence between it and CFT, and we all know being safe and conservative isn't my style when it comes to developing new things.

>>8990758
Girl (male)

>>8967329
>is it still useful in modern times?
Cute question anon.
The fact that logs make multiplication into addition is the historical motivation for why they're found. There are other important consequences of that that are useful in both mathematics and physics.