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.

8 pages, to appear in PRD

References in corpus (3)

• The Standard Model of Particles and Forces in the Framework of 2T-physics
• A Lagrangian for DSR Particle and the Role of Noncommutativity
• Yang's Quantized Space-time Algebra and Holographic Hypothesis

Cited by in corpus (10)

• The Area Quantum and Snyder Space
• 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
• Relativistic Particles on Quantum Space-time
• Entanglement in phase-space distribution for an anisotropic harmonic oscillator in noncommutative space
• Running anti-de Sitter radius from QCD-like strings
• Tuning the separability in noncommutative space
• Energy-momentum non-conservation on noncommutative spacetime and the existence of infinite spacetime dimension
• Space-Time Diffeomorphisms in Noncommutative Gauge Theories