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

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, $\eta$, namely $\sqrt{\eta }\lesssim 10^{-12}eV/c$. Additionally, a putative metric structure for the noncommutative phase-space is discussed.

18 pages

References in corpus (4)

• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems
• Phase-space noncommutative formulation of Ozawa's uncertainty principle
• Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle