2002/11/04 by Giovanni Amelino-Camelia, Francesco D'Andrea, Gianluca Mandanici · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Causality (physics) #Dispersion relation #Lorentz covariance #Momentum (technical analysis) #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Noncommutative quantum field theory #Quantum Electrodynamics and Casimir Effect #Realization (probability) #Relation (database) #Spacetime #hep-th
paper · pdf · doi:10.1088/1475-7516/2003/09/006
published as JCAP 0309 (2003) 006 · 13 pages, LaTex
arxiv created 2002/11/04 · openalex publication_date 2003/09/16 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The realization that forthcoming experimental studies, such as the ones planned for the GLAST space telescope, will be sensitive to Planck-scale deviations from Lorentz symmetry has increased interest in noncommutative spacetimes, in which this type of effect is expected. We focus here on κ-Minkowski spacetime, a much-studied example of Lie-algebra noncommutative spacetime, but our analysis appears to be applicable to a more general class of noncommutative spacetimes. A technical controversy which has significant implications for experimental testability is the one concerning the κ-Minkowski relation between group velocity and momentum. A large majority of studies adopted the familiar relation v = d E ( p )/d p , where E ( p ) is the κ-Minkowski dispersion relation, but recently some authors advocated alternative formulae. While in these previous studies the relation between group velocity and momentum was introduced through ad hoc formulae, we rely on a direct analysis of wave propagation in κ-Minkowski. Our results lead conclusively to the relation v = d E ( p )/d p . We also show that the previous proposals of alternative velocity/momentum relations implicitly relied on an inconsistent implementation of functional calculus on κ-Minkowski and/or on an inconsistent description of spacetime translations.