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Noncommutative Symmetries and Gravity

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Noncommutative Spacetimes

Part of the book series: Lecture Notes in Physics ((LNP,volume 774))

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Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star multiplied. Consistently, spacetime diffeomorphisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincaré transformations is defined and explicitly constructed. We can then define covariant derivatives (that implement the principle of general covariance on noncommutative spacetime) and torsion and curvature tensors. With these geometric tools we formulate a noncommutative theory of gravity.

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  1. INFN Torino, Alessandria, Italy

    Paolo Aschieri

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Aschieri, P. (2009). Noncommutative Symmetries and Gravity. In: Noncommutative Spacetimes. Lecture Notes in Physics, vol 774. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89793-4_8

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  • DOI: https://doi.org/10.1007/978-3-540-89793-4_8

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