Friday, July 12, 2013

1307.2940 (Theo Johnson-Freyd)

A combinatorial universal $\star$-product    [PDF]

Theo Johnson-Freyd
We construct combinatorially a canonical universal $\star$-quantization of infinitesimal Poisson manifolds equipped with affine coordinates. Our construction improves the existing celebrated result by Kontsevich in two ways. First, we avoid all period integrals and other transcendental techniques, so that the coefficients of our $\star$-quantization are rational numbers. Second, we use no "wheels," so that our quantization is defined in infinite dimensions and in other settings where traces are undefined. Our construction relies on the theory of Koszul duality for properads, and also uses a "quasilocal" version of factorization algebras and effective quantum field theory.
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