Noncommutative spaces, the quantum of time and the Lorentz symmetry

Abstract

We introduce three space-times that are discrete in time and compatible with the Lorentz symmetry. We show that these spaces are no commutative, with commutation relations similar to the relations of the Snyder and Yang spaces. Furthermore, using a reparametrized relativistic particle we obtain a realization of the Snyder type spaces and we construct an action for them.

arXiv comment8 pages, to appear in PRD

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Cited by in corpus (13)

• Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space
• The Area Quantum and Snyder Space
• Noncommutative Geometry and Fluid Dynamics
• Deformed phase space in a two dimensional minisuperspace model
• On the two-dimensional time-dependent anisotropic harmonic oscillator in a magnetic field
• A fundamental length as a candidate for dark energy: a DSR inspired FRW spacetime
• A cosmological viewpoint on the correspondence between deformed phase-space and canonical quantization
• Relativistic Particles on Quantum Space-time
• Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space
• Tuning the separability in noncommutative space
• Space-Time Diffeomorphisms in Noncommutative Gauge Theories
• Running anti-de Sitter radius from QCD-like strings
• Energy-momentum non-conservation on noncommutative spacetime and the existence of infinite spacetime dimension