Seminar by Niels Leth Gammelgaard

Title: Combinatorics of Deformation Quantization on Kähler Manifolds

2013.09.11 | Christine Dilling

Date Wed 30 Oct
Time 15:15 16:15
Location Aud. D3

Abstract

Deformation quantization attempts to encode the non-commutative behaviour of quantum observables through a deformation, called a star product, of the usual pointwise product in the Poisson algebra of functions on a symplectic manifold. In the presence of a compatible complex structure on the symplectic manifold, all star products (respecting the complex structure) can be completely classified (not only up to equivalence) by their Karabegov form. In this talk, I will show how to recover, from its classifying Karabegov form, a completely explicit formula for any star product. The formula uses Feynman graphs to encode differential operators in local coordinates, and the proof relies purely on combinatorial manipulations of the graphs. If time permits, I will also discuss the problem of giving a formula in global terms.

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