/sci/ - Science & Math

if anime/touhu, at least make it math

Can someone provide me with applications of these subjects in theoretical physics? They seem quite hard and i'd like to know if its worth it to study them.

Can someone provide me with the applications these subject have in theoretical physics? They seem quite hard and i'd like to know if its worth it to study them.

>>9736716
His method of teaching gives you the concrete intuition needed for true understanding instead of jumping straight into unmotivated formalism and walls of notation/abstraction. I guess that's a bad thing for those people who like to hide behind walls of abstraction to prevent deeper empirical understand of the subjects involved. Some would even argue that he introduces these incomprehensibly abstract concepts too early. Also, I am willing to bet that you can't even draw a picture of a cofibration. We usually discourage this kind of learning in the TQFT community and obviously for good reasons. I guess the "mathematicians" still have a lot of catching up to do. This is especially clear if you look at the whole homotopy "hypothesis" situation.
>>9736729
I was recently reading his correspondence with Grothendieck regarding the whole homotopy "hypothesis" fiasco. He had pretty profound views on the subject, as expected of a true empirical mind. Maybe we can hope that "mathematicians" will catch up if we give them about 50-60 years. Maybe then they would actually be able to present a proper proof of this homotopy "hypothesis". Me and my adviser think not, because the cobordism hypothesis is the cornerstone of something concrete (i.e. TQFT, string theory) while this homotopy "hypothesis" is the cornerstone of absolute algebraic wank.
Basically, I suggest reading Von Neumann - Mathematical Foudnations of Quantum Mechanics to develop the necessary prerequisites for looking into these things at a deeper level. Then read Lurie's and Sakurai's elementary proof of the cobordism hypothesis, it should be somewhere on arxiv. If you have any questions about the physical intuitions involved in understanding the proof, feel free to post them here. You need to develop proper intuitions so you don't mistakenly believe that the results they obtain are "spooky" and "unphysical".

>>9461227
>perturbative
>algebraic
I've never seen that desu. My field is TQFT and CFT so I might be wrong on some recent developments in AQFT so can't help you much there.

I'm interested in studying mathematical physics after graduating. Where do you reckon is easier to get a scholarship? Which are the best institutes/universities for the subject?

>I can't tell if /sci/ is being raided by CS troll threads or carrying on as usual.
>Will someone please tell me what is going on?
>>9396213
I see he's a fellow Taiwanese.

>>9388176
In the presence of scaling symmetry near the critical point you can write the energy-momentum tensor as a holomorphic part and an antiholomorphic part, which can be evaluated using contour integrals. Then you can build up the generators of the conformal symmetry with this using Cauchy integral formula
[math]L_n(z) = \int_\gamma \frac{dw}{(z-w)^{n+1}}T(w)[/math] as well as its dual part [math]\overline{L}_n[/math], and from the commutation relations of [math]T[/math] you can deduce the commutation relations of the generators [math]L_n[/math], which turns out to be the Virasoro algebra [math][L_n,L_m] =
L_{n+m} + \delta_{n+m}\frac{c}{12}[/math]. Given a simple Lie algebra [math]\mathfrak{g}[/math], the generators form the basis for the affine Lie algebra [math]\mathfrak{g}_\mathbb{C} = (\mathfrak{g}^+ \otimes \mathfrak{g}^-) \oplus c \mathbb{C}[/math] of [math]\mathfrak{g}[/math], where [math]\mathfrak{g}^+[/math] is generated by [math](L_n,f), f \in \mathbb{C}((z))[/math] and [math]\mathfrak{g}^-[/math] by [math](\overline L_n,f), f \in \mathbb{C}((z))[/math], where [math]\mathbb{C}((z))[/math] is the algebra of Laurent series in [math]z[/math] (you can generalized this to sheaves of Laurent series [math]\mathcal{O}_R[/math] on a Riemann surface [math]R[/math]). The Verma module that describes the physical states are then defined to be the set of vectors [math]v \in V[/math] such that [math]U(\mathfrak{g}^+)v =
0[/math], and the "primary field operators" of the CFT lie within the loop subgroup [math]LG^+[/math] of the loop group [math]LG[/math] of the central extension [math]\hat{\mathfrak{g}}_\mathbb{C}[/math] of the affine Lie algebra [math]\mathfrak{g}_\mathbb{C}[/math] of the Lie algebra [math]\mathfrak{g}[/math].
It is then possible to define a Hitchin's connection on [math]LG^+[/math], the flatness condition of which gives rise to the KZ equations, and these are the equations that your conformal blocks satisfy.

>>9348558
>any pro tips or guides?
Can't tell you since I've never used any.
>who is your favorite 2hu?
Ran is qt.
>Where do I start to unlock your subterranean autism?
Get one of those IQ increasing drugs from Eirin or something lmao.
>[math]\mathfrak{which}~\mathfrak{ touhou}~\mathfrak{ h}-\mathfrak{doujins}~\mathfrak{ do}~\mathfrak{ you}~\mathfrak{ prefer}[/math]
I liked the one where Yukari and Yuyuko raped this one village boy.