Noncommutative Spaces and Poincaré Symmetry

Stjepan Meljanac, Daniel Meljanac, Flavio Mercati, Danijel Pikutić

Published 2016-10-21Version 1

We present a framework which unifies a large class of non-commutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the coordinates, with structure constants depending on the momenta plus terms depending only on the momenta. The possible implementations of the action of Poincar\'e transformations on these deformed phase spaces are considered, together with the consistency requirements they introduce. It is found that Lorentz transformations in general act nontrivially on tensor products of momenta. In particular, a 'backreaction' effect needs to be considered, which changes in a momentum-dependent way the Lorentz group element which acts on the left and on the right of a composition of two momenta. We conclude with two representative examples, which illustrate the 'backreaction' effect.