Noncommutative gauge theory for Poisson manifolds. (English) Zbl 0984.81167

Summary: A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich’s formality theorem.


81T75 Noncommutative geometry methods in quantum field theory
81T13 Yang-Mills and other gauge theories in quantum field theory
53D17 Poisson manifolds; Poisson groupoids and algebroids
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