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Results tagged with mp.mathematical-physics
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user 582
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
4
votes
Who can tell me the properties for the delta function in Sato's theory?
In addition to Kac's excellent book I thought I'd mention Vertex algebras and algebraic curves by Ed Frenkel and me, which goes a little more into formal delta functions, D-modules and the like --- se …
- 24.1k
79
votes
What is the motivation for a vertex algebra?
Vertex algebras precisely model the structure of "holomorphic one-dimensional algebra" -- in other words, the algebraic structure that you get if you try to formalize the idea of operators (elements o …
- 24.1k
3
votes
Accepted
Mirror symmetries for generalized geometries ?
Mirror symmetry is at the most fundamental level an isomorphism of N=(2,2)-supersymmetric conformal field theories attached to different geometric data, which acts on the supersymmetries as a prescrib …
- 24.1k
14
votes
About state-field correspondence
I want to elaborate a little on Pavel's excellent answer.
We can think (very schematically) of local operators in an n-dimensional
field theory the following way. We have an n-1 manifold M with some …
- 24.1k
6
votes
About topological B model
This is the subject of this paper by Kevin Costello -- he constructs a solution to a master equation associated to a Calabi-Yau category, which one could take to be the category of branes in the topol …
- 24.1k
13
votes
Mirror symmetry mod p?! ... Physics mod p?!
The most interesting answer I know to this question is the recent work of Albert Schwarz with Vadim Vologodsky, Ilya Shaprio and Maxim Kontsevich, in which for example they use properties of the Frobe …
- 24.1k
15
votes
Accepted
Higher genus closed string B-model
This is a great question I wish I understood the answer to better.
I know two vague answers, one based on derived algebraic geometry and one based on string theory.
The first answer, that Costello exp …
- 24.1k
5
votes
Path integral derivation of extended TQFT
The original motivation for extended TQFTs (as introduced by Freed, Lawrence, Baez-Dolan) is indeed giving a finer form of locality, as explained by Dmitri Pavlov. However I think there are two quicke …
- 24.1k
13
votes
Relationship between the TQFTs in Kapustin-Witten and Ben-Zvi-Sakellaridis-Venkatesh
The (fairly poetic and ill-formed) idea in this story is that the Kapustin-Witten story and the Langlands program are about the SAME four-dimensional TQFTs, but evaluated on different "manifolds" - i. …
- 24.1k
19
votes
Accepted
Implications and consequences of the recent proof of the geometric Langlands conjecture
To avoid writing a long essay I'll be very telegraphic.
Here are some of the many open problems that are reasonably "next" in the area. I'll use [GLC] to refer to the recent papers proving the unramif …
- 24.1k