/sci/ - Science & Math

>>11402435
Just some things I do
>lifting/exercise
>hike/camp with friends
>play violin in orchestra
>go out with my fiance

>Will I find happiness at the end of my path
If all you do is math? No lol.

>>11159995
Some of these I have already answered. Specifically >>11149157 and >>11147127. However the posts seemed to be deleted by quality-hating jannies but you can check out my answer by referencing the replies to it.
>>11155503
By definition, virtual particles are unobservables that oscillate beyond the energy scale of the problem; in other words, they're the "inner edges" of the Feynman diagrams. For instance, radiative corrections all stem from exchange of virtual particles which make QED amplitudes diverge in the IR limit. They oscillate with wavenumber much beyond those restricted by momentum conservation across the vertices.
>>11160679
No.

>>11065704
We take a [math]k[/math]-jet to be an equivalence class of functions [math]\varphi,\psi \in C^\infty(M)[/math] on a smooth manifold [math]M[/math] such that [math]\partial^r \varphi = \partial^r \psi[/math] for [math]r < k[/math] (up to a constant factor). The point-wise equivalence relation defines a vector space of [math]k[/math]-jets, and this forms the fibres of the [math]k[/math]-jet bundle [math]J^kM[/math] on [math]M[/math].
We then take the inductive limit [math]k\rightarrow \infty[/math] to get the jet bundle [math]J^\infty M[/math]. Intuitively for analytic functions, fibres are basically "evaluations of fields and their derivatives".

>>11007700
Yep, no harm in trying, except for the $150 application fee lmao

>>10155575
Existence of Mazur manifolds whose inner product inherited from the extended unitary 4-TQFT vanishes.

>>9480724
Spectral sequences (e.g. Leray, Gysin, etc) can be used to evaluate hypercohomology groups of sheaves, which characterize diffeomorphism classes of Hermitian line bundles on paracompact (or ILH) spaces. These diffeomorphism classes present obstructions (the [math]H^1[/math] and [math]H^2[/math] terms) to the existence of quantomorphisms (lifts of symplectomorphisms onto Hermitian line bundles) via Kostant's construction, as well as obstructions (the [math]H^3[/math] term of the Hochschild cohomology) to deformation quantization a la Weyl-Moyal. These quantization conditions are necessary (and sufficient in the case of symplectic manifolds) conditions for your manifold to have "quantizable" physical observables.

>>9460883
>that is actually readable
What isn't readable to you?