Observables and dispersion relations in κ-Minkowski spacetime

• Published in: The journal of high energy physics Vol. 2017; no. 10; pp. 1 - 27
• Main Authors: Aschieri, Paolo, Borowiec, Andrzej, Pachoł, Anna
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2017; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Deformation; Elementary Particles; High energy physics; Lie groups; Non-Commutative Geometry; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Groups; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity; Relativity Theory; Space-Time Symmetries; Spacetime; String Theory; Transformations (mathematics); Translations; Wave dispersion; Wave equations; Non-Commutative Geometry; Quantum Groups; Space-Time Symmetries
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2017)152

A bstract We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of κ -Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d’Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.