Noncommutative Spaces and Poincaré Symmetry

Abstract

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 Lorentz 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 the Lorentz group element which acts on the left and on the right of a composition of two momenta is different, and depends on the momenta involved in the process. We conclude with two representative examples, which illustrate the mentioned effect.

7 pages, to be published in Phys. Lett. B

References in corpus (6)

• Twisted Statistics in kappa-Minkowski Spacetime
• Relativistic kinematics beyond Special Relativity
• Noncommutativity due to spin
• Beyond Special Relativity at second order
• Algebraic approach to quantum gravity II: noncommutative spacetime
• Exploring Special Relative Locality with deSitter momentum-space

Cited by in corpus (9)

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• $k$-Minkowski-deformation of $U(1)$ gauge theory
• Generalizations of Snyder model to curved spaces
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Noncommutative Yang model and its generalizations
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Noncommutative spacetime symmetries from covariant quantum mechanics