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Vectorlike deformations of relativistic quantum phase-space and relativistic kinematics

Niccoló Loret

Division of Theoretical Physics, Ruđer Bošković Institute, Bijenička c.54, HR-10002 Zagreb, Croatia

E-mail Address: niccolo@accatagliato.org

E-mail Address: Niccolo.Loret@irb.hr

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Stjepan Meljanac

Division of Theoretical Physics, Ruđer Bošković Institute, Bijenička c.54, HR-10002 Zagreb, Croatia

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Flavio Mercati

Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, Canada N2L 2Y5, Canada

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, and

Danijel Pikutić

Division of Theoretical Physics, Ruđer Bošković Institute, Bijenička c.54, HR-10002 Zagreb, Croatia

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https://doi.org/10.1142/S0218271817501231Cited by:12 (Source: Crossref)

Abstract

We study a family of noncommutative spacetimes constructed by one four-vector. The large set of coordinate commutation relations described in this way includes many cases that are widely studied in the literature. The Hopf-algebra symmetries of these noncommutative spacetimes, as well as the structures of star product and twist are introduced and considered at first order in the deformation, described by four parameters. We also study the deformations to relativistic kinematics implied by this framework, and calculate the most general expression for the momentum dependence of the Lorentz transformations on momenta, which is an effect that is required by consistency. At the end of the paper we analyse the phenomenological consequences of this large family of vectorlike deformations on particles propagation in spacetime. This leads to a set of characteristic phenomenological effects.

Keywords:

PACS: 02.20.Uw, 02.40.Gh, 04.60.−m, 04.60.Bc

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