Shadow of noncommutativity

Abstract

We analyse the structure of the $\kappa =0$ limit of a family of algebras $A_{\kappa }$ describing noncommutative versions of space-time, with $\kappa$ a parameter of noncommutativity. Assuming the Poincaré covariance of the $\kappa =0$ limit, we show that, besides the algebra of functions on Minkowski space, $A_0$ must contain a nontrivial extra factor $A_0^I$ 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.

19 pages, Latex2e, available at http://qcd.th.u-psud.fr

References in corpus (1)

• The quantum structure of spacetime at the Planck scale and quantum fields

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