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.

arXiv comment18 pages

References in corpus (20)

• Modern tests of Lorentz invariance
• Noncommutative Field Theory and Lorentz Violation
• The Fermi GBM Gamma-Ray Burst Spectral Catalog: Four Years Of Data
• The 2nd Fermi GBM Gamma-Ray Burst Catalog: The First Four Years
• The 3rd Fermi GBM Gamma-Ray Burst Catalog: The First Six Years
• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems
• Aspects of Phase-Space Noncommutative Quantum Mechanics
• Phase-Space Noncommutativity and the Dirac Equation
• Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit
• Entanglement due to noncommutativity in the phase-space
• Phase-space noncommutative formulation of Ozawa's uncertainty principle
• Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors
• Robertson-Schroedinger type formulation of Ozawa's noise-disturbance uncertainty principle
• Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
• Threshold Effects and Lorentz Symmetry
• Gravity as the breakdown of conformal invariance
• Coherent quantum squeezing due to the phase space noncommutativity
• Observational Constraints on Local Lorentz Invariance
• Generalized Noether theorem in the realm of Hamiltonian point dynamics

Cited by in corpus (4)

• Heat flow and noncommutative quantum mechanics in phase-space
• Noncommutative phase-space effects in thermal diffusion of Gaussian states
• Quantum cloning and teleportation fidelity in the noncommutative phase-space
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries