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Noncommutative gauge theory for Poisson manifolds

Branislav Jurco·Peter Schupp·Julius Wess
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Abstract

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.

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Branislav Jurco, Peter Schupp, Julius Wess. 2000-05-12. Noncommutative gauge theory for Poisson manifolds. https://doi.org/10.1016/s0550-3213(00)00363-1

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