Multi-particle systems in quantum spacetime and a novel challenge for center-of-mass motion

Abstract

In recent times there has been considerable interest in scenarios for quantum gravity in which particle kinematics is affected nonlinearly by the Planck scale, with encouraging results for the phenomenological prospects, but also some concerns that the nonlinearities might produce pathological properties for composite/multiparticle systems. We here focus on kinematics in the $\kappa$-Minkowski noncommutative spacetime, the quantum spacetime which has been most studied from this perspective, and compare the implications of the alternative descriptions of the total momentum of a multiparticle system which have been so far proposed. We provide evidence suggesting that priority should be given to defining the total momentum as the standard linear sum of the momenta of the particles composing the system. We also uncover a previously unnoticed feature concerning some (minute but conceptually important) effects on center-of-mass motion due to properties of the motion of the constituents relative to the center of mass.

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• The quantum structure of spacetime at the Planck scale and quantum fields
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• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Quantum Spacetime Phenomenology
• Classical and Quantum Mechanics of Free \k Relativistic Systems
• The principle of relative locality
• Lorentz violation at high energy: concepts, phenomena and astrophysical constraints
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• Relative locality and the soccer ball problem
• Relative locality in a quantum spacetime and the pregeometry of $\kappa$-Minkowski

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• Weak equivalence principle and nonrelativistic limit of general dispersion relations
• Non-local imprints of gravity on quantum theory