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.