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    We examine some alternative possibilities for an action functional for κ-Minkowski noncommutative space–time. Early works on κ-Minkowski focused on κ-Poincaré covariance and the dependence of the action functional on the choice of Weyl map, renouncing to invariance under cyclic permutations of the factors composing the argument of the action functional. It has been recently suggested, focusing on a specific choice of Weyl map and setting aside the issue of κ-Poincaré covariance of the action functional, that a cyclicity-inducing measure could be introduced in implicit form. We provide an explicit formula for (and derivation of) a choice of measure which indeed ensures cyclicity of the action functional. The same choice of measure is applicable to all the most used choices of Weyl map, but we find that this "cyclicity-inducing measure" is not invariant under κ-Poincaré transformations. We also notice that the cyclicity-inducing measure can be straightforwardly derived using a map which connects the κ-Minkowski space–time coordinates and the space–time coordinates of a "canonical" noncommutative space–time, with coordinate-independent commutators.


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