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Noncommutative Gauge Theories from Deformation Quantization

Tsuguhiko Asakawa·Isao Kishimoto
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Abstract

We construct noncommutative gauge theories based on the notion of the Weyl bundle, which appears in Fedosov's construction of deformation quantization on an arbitrary symplectic manifold. These correspond to D-brane worldvolume theories in non-constant B-field and curved backgrounds in string theory. All such theories are embedded into a "universal" gauge theory of the Weyl bundle. This shows that the combination of a background field and a noncommutative field strength has universal meaning as a field strength of the Weyl bundle. We also show that the gauge equivalence relation is a part of such a "universal" gauge symmetry.

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Tsuguhiko Asakawa, Isao Kishimoto. 2000-11-22. Noncommutative Gauge Theories from Deformation Quantization. https://doi.org/10.1016/s0550-3213(00)00433-8

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