Shadow of noncommutativity

Abstract

We analyse the structure of the $κ=0$ limit of a family of algebras $A_κ$ 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, $A_0$ must contain a nontrivial extra factor $A^I_0$ 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 analyse some representative examples.