Noncommutative Differential Forms on the kappa-deformed Space

Details Noncommutative Differential Forms on the kappa-deformed Space Noncommutative Differential Forms on the kappa-deformed Space

2008-12-24

arxiv.org/abs/0812.4571v2

J.Phys. A 42 (2009) 365204

Physics

High Energy Physics

High Energy Physics - Theory

to appear in J. Phys. A: Math. Theor

Scientific paper

10.1088/1751-8113/42/36/365204

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of the noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher-order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded-commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well-defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.

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