# Relativistic dispersion relation and putative metric structure in noncommutative phase-space

Leal, P.  (Departamento de Física e Astronomia and Centro de Física do Porto, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal) ; Bertolami, O. (Departamento de Física e Astronomia and Centro de Física do Porto, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal)

24 April 2019

Abstract: The deformation of the relativistic dispersion relation caused by noncommutative (NC) Quantum Mechanics (QM) is studied using the extended phase-space formalism. The introduction of the additional commutation relations induces Lorentz invariance violation. It is shown that this deformation does not affect the propagation speed of free massless particles. From the deformation of the dispersion relation for massless particles, gamma ray burst data is used to establish an upper bound on the noncommutative parameter, η , namely η≲10−12eV/c . Additionally, a putative metric structure for the noncommutative phase-space is discussed.

Published in: Physics letters B (2019)