Gauge field theories with covariant star-product
arXiv:0905.0608 · doi:10.1088/1126-6708/2009/07/084
Abstract
A noncommutative gauge theory is developed using a covariant star-product between differential forms defined on a symplectic manifold, considered as the space-time. It is proven that the field strength two-form is gauge covariant and satisfies a deformed Bianchi identity. The noncommutative Yang-Mills action is defined using a gauge covariant metric on the space-time and its gauge invariance is proven up to the second order in the noncommutativity parameter.
Dedicated to Ioan Gottlieb on the occasion of his 80th birthday anniversary. 12 pages
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