Noncommutative Symmetries and Gravity

Physics – High Energy Physics – High Energy Physics - Theory

Scientific paper

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26 pages. Lectures given at the workshop `Noncommutative Geometry in Field and String Theories', Corfu Summer Institute on EPP

Scientific paper

10.1088/1742-6596/53/1/052

Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincare' transformations is defined and explicitly constructed. This allows to construct a noncommutative theory of gravity.

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