Noncommutative gauge theory using covariant star product defined between Lie-valued differential forms
arXiv:1001.0508 · doi:10.1103/PhysRevD.81.085026
Abstract
We develop an internal gauge theory using a covariant star product. The space-time is a symplectic manifold endowed only with torsion but no curvature. It is shown that, in order to assure the restrictions imposed by the associativity property of the star product, the torsion of the space-time has to be covariant constant. An illustrative example is given and it is concluded that in this case the conditions necessary to define a covariant star product on a symplectic manifold completely determine its connection.
AMS-LaTeX 19 pages. v2: corrections in language and equations (typos), expanded sections 3-5, added references. v3: minor presentational and grammatical corrections, completed, corrected and reordered some references.
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Cited by in corpus (10)
- Gauge theories on quantum spaces
- On some models of geometric noncommutative general relativity
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- Emergent Noncommutative gravity from a consistent deformation of gauge theory
- Covariant star product on symplectic and Poisson spacetime manifolds
- Gravity in Extreme Regions Based on Noncommutative Quantization of Teleparallel Gravity
- Field Theory with Coordinate Dependent Noncommutativity
- Seiberg-Witten Map with Lorentz-Invariance and Gauge-Covariant Star Product
- A note on the implementation of Poincaré symmetry in noncommutative field theory
- Covariant Star Product on Semi-Conformally Flat Noncommutative Calabi-Yau Manifolds and Noncommutative Topological Index Theorem