Time Discretization From Noncommutativity

Abstract

We show that a particular noncommutative geometry, sometimes called angular or $\rho$-Minkowski, requires that the spectrum of time be discrete. In this noncommutative space the time variable is not commuting with the angular variable in cylindrical coordinates. The possible values that the variable can take go from minus infinity to plus infinity, equally spaced by the scale of noncommmutativity. Possible self-adjoint extensions of the "time operator" are discussed. They give that a measurement of time can be any real value, but time intervals are still quantized.

arXiv comment13 pages, one figure. Substantially enlarged with references added

References in corpus (25)

• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• The principle of relative locality
• New Lie-Algebraic and Quadratic Deformations of Minkowski Space from Twisted Poincare Symmetries
• Zeptosecond Birth Time Delay in Molecular Photoionization
• Space-Time Noncommutativity, Discreteness of Time and Unitarity
• Real Forms of Complex Quantum Anti de Sitter Algebra $U_q(Sp(4,C))$ and their Contraction Schemes
• Noncommutative Supersymmetric Tubes
• Infinitely many star products to play with
• Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions
• Noncommutative BTZ Black Hole and Discrete Time
• Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole
• Noncommutative field theory from angular twist
• Localization and Reference Frames in $\kappa$-Minkowski Spacetime
• Noncommutative scalar field in the non-extremal Reissner-Nordström background: QNM spectrum
• Spectral geometry with a cut-off: topological and metric aspects
• Split noncommutativity and compactified brane solutions in matrix models
• Modeling transverse relative locality
• Matrix Bases for Star Products: a Review
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• Discrete Time from Quantum Physics
• The Kappa-Weyl group and its algebra
• $\mathcal{P}\mathcal{T}$-symmetric quantum field theory on the noncommutative spacetime
• Discrete Time Evolution and Energy Nonconservation in Noncommutative Physics
• Time, classical and quantum
• Search for footprints of quantum spacetime in black hole QNM spectrum

Cited by in corpus (11)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Poisson gauge models and Seiberg-Witten map
• Localization and observers in $\varrho$-Minkowski spacetime
• Double Quantization
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Fingerprints of the quantum space-time in time-dependent quantum mechanics: An emergent geometric phase
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Field theories on $\rho$-deformed Minkowski space-time
• A Stochastic Origin of Spacetime Non-Commutativity
• Star-products for Lie-algebraic noncommutative Minkowski space-times
• Four-dimensional noncommutative deformations of $U(1)$ gauge theory and $L_{\infty }$ bootstrap