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Combinatorics of Deformation Quantization on Kähler Manifolds

Niels Leth Gammelgaard
Wednesday, 30 October, 2013, at 15:15-16:15, in Aud. D3 (1531-215)
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.
Organised by: QGM
Contact person: Jørgen Ellegaard Andersen