23/02/13 15:46:49.46 xsCTjZGt.net
>>376
>URLﾘﾝｸ(mathoverflow.net)
>What is the motivation for a vertex algebra?
追加引用 (回答のDavid Ben-Zvi氏は、Edward Frenkel氏からみの大物だね（後述）)
8 Answers
75 answered Feb 1, 2011 David Ben-Zvi
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 of your algebra) living at points of a Riemann surface, and get multiplied when you collide.
Our geometric understanding of how to formalize this idea has I think improved dramatically over the years with crucial steps being given by the point of view of "factorization algebras" by Beilinson and Drinfeld, which is explained (among other places :-) ) in the last chapter of my book with Edward Frenkel, "Vertex algebras and algebraic curves" (second edition only). This formalism gives a great way to understand the algebraic structure of local operators in general quantum field theories -- as is seen in the recent work of Kevin Costello -- or in topological field theory, where it appears eg in the work of Jacob Lurie (in particular the notion of "topological chiral homology").
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