Vector-like deformations of relativistic quantum phase-space and relativistic kinematics

TL;DR

This paper explores a broad family of noncommutative spacetimes characterized by vector-like deformations, analyzing their algebraic structures, symmetries, and implications for relativistic kinematics and particle phenomenology.

Contribution

It introduces a general framework for vector-like noncommutative spacetimes, including their algebraic structures, symmetries, and phenomenological consequences, extending previous specific models.

Findings

Derived the most general momentum-dependent Lorentz transformations.

Analyzed the star product and twist structures at first order in deformation.

Identified characteristic phenomenological effects on particle propagation.

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 vector-like deformations on particles propagation in spacetime. This leads to a set of characteristic phenomenological effects.