/sci/ - Science & Math

>>15868916
>I estimate
Got any napkin math for us to look at?

>>15842566
Cunnyfag pls go, this is a hag board

>>15536002
>is this you yukarifag
Pardon the tripfagging, but I am not the Yukarifag. I'm just /sci/'s manager for the 4cc.
Incidentally, Ed Witten is already on the team as the starting goalkeeper and I made that video.
>please post all the tohou math edits
I'll post all the ones I've got, I doubt my collection is exhaustive.

>>15190942
>Nobody here even has a bachelor's degree, let alone a PhD in physics or math.
On the contrary they do, who do you think all the shitposters are?

>>15187034
I'll give you what I have, did you save the ones from my thread?
I'd also be interested in the ones that you have

>>11805961
Anime is inherently mathematical.

>>11515249
The other answers seem to be missing the physical ingredients.
In general we start with the (generally field-theoretic) Hamilton-Jacobi equation [math]\delta_\Phi S_E(\delta \Psi,\Psi) = 0[/math] on [math]L^2(\mathcal{A})[/math] with [math]S_E[/math] the Euclidean action, where [math]\mathcal{A}[/math] is the space of "boundary conditions" (i.e. field-theoretic data on codim-1 submanifolds [math]\Sigma[/math]). Completing [math]\mathcal{A}[/math] it in the convolution product, we invoke GNS to obtain a *-representation [math]\mathcal{A}\rightarrow \mathcal{B}(\mathcal{H})[/math] on some Hilbert space [math]\mathcal{H}[/math] with a distinguished cyclic vacuum vector [math]|\Omega\rangle\in \mathcal{H}[/math] (in fact, GNS says that there is an equivalence between states [math]\Omega: A\mapsto \langle\Omega|A|\Omega\rangle \in \mathcal{B}(\mathcal{H})^*[/math] and *-representations into [math]\mathcal{B}(\mathcal{H})[/math]). For each "boundary wavefunction" [math]\Phi \in \mathcal{A}[/math], we wish to associate a state vector [math]|\Phi\rangle\in\mathcal{H}[/math] to the Schwinger functional [math]W[\Phi] = \int_{\Psi|_{\Sigma} = \Phi} D\Psi e^{-S_E[\Psi]} {\equiv}^{\star} \langle \Phi|\Omega\rangle[/math]. If this is doable, we can invoke the cyclicity of [math]|\Omega\rangle[/math] to write this as [math]\langle \Omega|\hat{\Phi}|\Omega\rangle[/math], where [math]\hat{\Phi}\in\mathcal{B}(\mathcal{H})[/math] is the second-quantized quantum field operator of [math]\Phi\in\mathcal{A}[/math] under the GNS *-representation. These state vectors [math]|\Phi\rangle\in\mathcal{H}[/math] are what we mean by the kets.
There are many [math]many[/math] mathematical subtleties to this construction of Schwinger correlations in QFT, however, but it is the foundation of non-perturbative methods in QFT.

>>11429156
Math is inherently anime.

>>11417945
Come. Let me show you

>>11403602
>yukarifag answered some of the physics stuff but his posts got vanished
Yep. These (>>11388946, >>11389028) I have already answered but were deleted for no reason.
>>11394388
First of all the dihedrals have rotation and reflections as generators. Since rotations commute you know any non-Abelianness must come from stuff involving reflections. First place to check then is to compute [math][r^p,sr^q][/math] for some [math]p,q\in \mathbb{Z}_k[/math].
On the other hand you can also look at gradings [math]c: D_{2n}\rightarrow\mathbb{Z}_2 \in H^1(D_{2n},\mathbb{Z}_2)[/math]. With [math]\mathbb{Z}_2 = \{\pm 1\}[/math] written multiplicatively, it is Abelian hence any section [math]s:\mathbb{Z}_2\rightarrow D_{2n}[/math] such that [math]sc = \operatorname{id}_{\mathbb{Z}_2}[/math] has the centre as the image.
>>11391694
Find the electric potential [math]\phi[/math], which solves the Dirichlet problem [math]\nabla\phi = \delta_R[/math] with BC [math]\phi(\infty)=0[/math], where [math]\delta_R[/math] is the delta function on the ring [math]R\subset\mathbb{R}^3[/math]. Kirchoff's integral formula then allows you to explicitly compute [math]\phi[/math] (hint: use cylindrical coordinates) then you just take [math]{\bf E} = -\nabla \phi[/math].

>>11350628
https://arxiv.org/abs/1712.02952

>>11182283
I'll post the answer sheet tomorrow.

>>11013037
I don't follow Vafa's non-categorical/cosmological stuff but his work in general won't be something that's significant only in the scope of string theory, and I doubt that's his motivation to begin with.
The only bombshell I could imagine him putting out in my limited expertise is some extremely powerful [math]C[/math]-theorem for (2,0) interacting 6D superconformal that characterizes all of its compactification IR fixed points and unifies every SuGra under the sun, which I definitely wouldn't put it past him.

>>10953156
>because going to Gensokyo after death is one possibility.
You'll need to pass the entrance exam first though.

>>10778817
Me. It deals with me.

>>10388601
It's natural to fear the unknown.

>>10223622
AdS/CFT is on very delicate foundations. One wrong move and it'll fall apart and Mandacena will disintegrate

>>10147486
First we notice that a fibre bundle [math]S^3 \rightarrow S^2[/math] with fibres [math]S^1[/math] over [math]S^2[/math] exists. Now the Pontrjagyn invariant [math]\mu:[S^2\times S^1,S^2]\rightarrow \mathbb{Z}_2[/math] characterizes homotopy classes of each local trivialization [math]S^2 \times S^1 \rightarrow S^2[/math]; the only non-trivial homotopy class is precisely the local trivializaiton of the Hopf fibration [math]S^3 \rightarrow S^2[/math]. To see why this is significant, the trivial bundle, characterized by [math]\mu = 0[/math], has unlinked fibres, while those for the Hopf fibration are linked: for each [math]x\neq y \in S^2[/math], the disjoint union [math]S^1_x \coprod S^2_y[/math] of the fibres over them is isotopic in [math]S^3[/math] to the Hopf link.
IN essence, the Hopf fibration is basically the [math]only[/math] non-trivial way to isometrically embed a bunch of circles parameterized by [math]S^2[/math] into [math]S^3[/math], up to homotopy.

I've also made this

>>10038057
I don't get your pics but ok