/sci/ - Science & Math

>>12565090
Sure did, got most of QG (covariant phase space) and susyST (Fukaya [math]D^\ast\text{Coh}(X)[/math]) as well under me. Once all the structure is in place, holography is just quantum duality plus some shift in interpretation. I'm now trying to categorify this notion via https://arxiv.org/abs/2005.14178

>>11376360
The scalar [math]\phi[/math] is only a semiclassical description of the coordinate sector [math]\phi(x) = \langle \phi|x\rangle[/math] of the electron state [math]|\phi\rangle[/math], so the surface tension analogy is strictly speaking independent of the statistics of the state. Fermions are in general sections of a spin bundle, so locally they consist of a spatial part [math]\phi \in C^\infty[/math] and a spinor part [math]\chi\in \operatorname{Cliff}[/math].

>>11322691
Note that [math]T\mathbb{R}^n[/math] is spanned by the differentials [math]\partial_i[/math], so as the Lie group of translations [math]\mathbb{R}^n[/math], the operators [math]\partial_i[/math] forms a basis for its Lie algebra. This is why [math]\exp\left(-ia^i \partial_i\right)f(x) = T_af(x) = f(x-a)[/math].
Or you can just assume [math]f\in L^2(\mathbb{T}^n,\mathbb{C})[/math] and do a Fourier transform, then compute from there.
>>11323513
Based and Connespilled.

>>11262090
Electrons in the same shell have the same energy, at least in the non-relativistic limit. Hence the number of electrons allowed in each shell corresponds to the rank of the irreps of [math]SU(2)[/math] labeled by eigenvalues [math]n \in \mathbb{Z}[/math] of the Casimir [math]L^2[/math].
>>11262254
They're saying that the DEs themselves don't change with time, not the quantities in the DEs. In other words, the strong-EL DE is the critical criterion for a time-translationally symmetric Lagrangian.

>>11060139
>it's gonna be alright.
Given how the thread has progressed over the past hour, I doubt it.

>>10986150
Mathematica & graph theory package.