Noncommutative Translations and $\star$-Product Formalism

Abstract

We consider the noncommutative space-times with Lie-algebraic noncommutativity (e.g. $\kappa$-deformed Minkowski space). In the framework with classical fields we extend the $\star$-product in order to represent the noncommutative translations in terms of commutative ones. We show the translational invariance of noncommutative bilinear action with local product of noncommutative fields. The quadratic noncommutativity is also briefly discussed.

LaTeX,ws-procs975x65 class (included), contribution to the Proceedings of the 11-th Marcel Grossmann meeting, Berlin, July 2006, Ed. H. Kleinert, R.T. Jantzen and R. Rufini, World Scientific, Singapore 2007. V2 small typo corrections

Cited by in corpus (1)

• star-Cohomology, Third Type Chern Character and Anomalies in General Translation-Invariant Noncommutative Yang-Mills