×

Multi-particle systems in quantum spacetime and a novel challenge for center-of-mass motion. (English) Zbl 1466.83064

Summary: 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.

MSC:

83C65 Methods of noncommutative geometry in general relativity
83C10 Equations of motion in general relativity and gravitational theory
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
16T05 Hopf algebras and their applications

References:

[1] Amelino-Camelia, G., Int. J. Mod. Phys. D11 (2002) 35. · Zbl 1062.83500
[2] Doplicher, S., Fredenhagen, K. and Roberts, J. E., Commun. Math. Phys.172 (1995) 187. · Zbl 0847.53051
[3] Bergmann, P. G. and Smith, G. J., Gen. Relativ. Gravit.14 (1982) 1131.
[4] Majid, S. and Ruegg, H., Phys. Lett. B334 (1994) 348. · Zbl 1112.81328
[5] Amelino-Camelia, G., Astuti, V. and Rosati, G., Eur. Phys. J. C73 (2013) 2521.
[6] Amelino-Camelia, G., Freidel, L., Kowalski-Glikman, J. and Smolin, L., Phys. Rev. D84 (2011) 084010.
[7] Gubitosi, G. and Mercati, F., Class. Quantum Grav.30 (2013) 145002. · Zbl 1273.83066
[8] Freidel, L. and Livine, E. R., Phys. Rev. Lett.96 (2006) 221301. · Zbl 1228.83047
[9] Amelino-Camelia, G., Living Rev. Relativ.16 (2013) 5.
[10] Amelino-Camelia, G., Freidel, L., Kowalski-Glikman, J. and Smolin, L., Phys. Rev. D84 (2011) 087702.
[11] Hossenfelder, S., SIGMA10 (2014) 074. · Zbl 1296.83007
[12] Amelino-Camelia, G., Entropy19 (2017) 400.
[13] Jacobson, T., Liberati, S. and Mattingly, D., Ann. Phys.321 (2006) 150. · Zbl 1086.85001
[14] Lukierski, J., Ruegg, H. and Zakrzewski, W. J., Ann. Phys.243 (1995) 90. · Zbl 0856.70012
[15] Amelino-Camelia, G., Symmetry4 (2012) 344. · Zbl 1351.81104
[16] Palmisano, M., Amelino-Camelia, G., Ronco, M. and D’Amico, G., Int. J. Mod. Phys. D29 (2020) 2050017.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.