/sci/ - Science & Math

>>11470635
Intrinsically? No. However the (screened) Coulomb potential reads [math]-\sum_k \frac{\lambda}{k^2+q^2}[/math] so coupling between particles with different momenta is possible through Coulomb.

>>11430146
>interesting
Not really. Projective spaces can be identified with [math]S^n/\mathbb{Z}_2[/math] and inherits the positive curvature metric from [math]S^2[/math] in the usual manner. Putting the horizon at infinity, it's quite literally how Renaissance/Baroque painters model their paintings with projective geometry.
>>11430216
Each free spin-1/2 encodes one quit.

>>10376798
Fuck. Replace every instance of [math]|\cdot|[/math] with [math]|\cdot|^2[/math] in my post. [math]4[/math] is the square of the norm.

>>10345945
Riesz & Sz-Nagi

>>9842838
>How could I compete
You don't.

>>9390511
>I was under the impression a Lie algebra describes *a* symmetry in the system.
This isn't always true, and even if it were it wouldn't mean Lie algebras has to describe symmetries anyway. In fact the special thing about CFTs is that the entirety of its operator algebra can be described by an affine Lie algebra [math]given[/math] its symmetries.
>Is there a short answer for how the Virasoro algebra connects to field operators and their commutation relations?
The Virasoro algebra defines a Verma module on which the algebra relations gives rise to KZ equations, and the solutions are the correlation functions (i.e. conformal blocks) of the primary fields.
>Also, is there a generator for scale transformations that fit in all this?
No, it's something else entirely. The translation, rotation and scaling symmetries are symmetries of the Hamiltonian which gives you the sufficient (and necessary) conditions to decompose it into anti-/holomorphic parts. That's the extent to which these symmetries are significant.
>Is there a generator for scale transformation?
Yes, and it's easily derived by putting [math]x^\mu \rightarrow x^\mu + \partial^\mu \epsilon(x)[/math] into the variation of the Hamiltonian.
There are several good books on the basics of CFT like DiFrancesco, Henkel, Kohno or Ueno that you can look into.
>>9390695
>What would you say is a priority in terms of fields of math for undergrad looking to get into mathematical physics?
Diff. top./geo., alg. top., functional analysis, group/representation theory, cohomology theory, Seiberg-Witten/Donaldson theory, Deligne-Mumford compactification, etc.
I don't know much about the institutes in the EU so I can't help you there.