engleski

Noncommutative Differential Forms on the kappa-deformed Space

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 not graded-commutative, but they satisfy the graded Jacobi identity. The star-product of classical differential forms is also defined. It is shown that the product depends on the realizations of both the noncommutative coordinates and one-forms on the kappa-deformed space. Owner: Sasa Kresic-Juric

differential form; kappa-deformed space; realization; Weyl algebra; exterior derivative

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