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Mathematics Colloquium


Date:  Tuesday, February 07, 2012

Title:  Algebraic structures in perturbative quantum field theory

Abstract:  Deformation quantization casts the problem of quantizing classical mechanical systems as an algebraic problem: given a Poisson algebra, find an associative algebra which is a quantization. I'll explain how the problem of quantizing a classical field theory can be expressed as a similar algebraic problem, using the language of factorization algebras. Then, I'll state a theorem describing the obstruction and deformation groups controlling possible quantizations, to each order in hbar. The proof of the theorem relies on the physicists' techniques of renormalization.

Speaker:  Kevin Costello
Institution:  Northwestern University


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