Shadow of noncommutativity

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Abstract
We analyze the structure of the κ=0 limit of a family of algebras Aκ describing noncommutative versions of space–time, with κ a parameter of noncommutativity. Assuming the Poincaré covariance of the κ=0 limit, we show that, besides the algebra of functions on Minkowski space, A0 must contain a nontrivial extra factor A0I which is Lorentz covariant and which does not commute with the functions whenever it is not commutative. We give a general description of the possibilities and analyze some representative examples.

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