A note about the quantum of area in a non-commutative space

Abstract

In this note we show that in a two-dimensional non-commutative space the area operator is quantized, this outcome is compared with the result obtained by Loop Quantum Gravity methods.

6 pages, references added, minor corrections

References in corpus (15)

• String Theory and Noncommutative Geometry
• Quantum Field Theory on Noncommutative Spaces
• Effective Field Theory, Black Holes, and the Cosmological Constant
• Noncommutative Perturbative Dynamics
• Bohr's Correspondence Principle and The Area Spectrum of Quantum Black Holes
• Loop Quantum Gravity
• Introduction to Modern Canonical Quantum General Relativity
• Quantum Gravity: a Progress Report
• Low-energy Limits on the Antisymmetric Tensor Field Background on the Brane and on the Non-commutative Scale
• Bounding Noncommutative QCD
• Physical Instances of Noncommuting Coordinates
• On area and entropy of a black hole
• BF gravity and the Immirzi parameter
• Spin Foam Models of Riemannian Quantum Gravity
• Spectral noncommutative geometry and quantization: a simple example

Cited by in corpus (14)

• On the "Universal" Quantum Area Spectrum
• Doubly Special Relativity in Position Space Starting from the Conformal Group
• The quantum of area $\Delta A=8\pi l_P^2$ and a statistical interpretation of black hole entropy
• Discreteness of area in noncommutative space
• Winding String Condensation and Noncommutative Deformation of Spacelike Singularity
• The Area Quantum and Snyder Space
• Quantum Black Holes: the Event Horizon as a Fuzzy Sphere
• Upper bound on the momentum scale in noncommutative phase space of canonical type
• Black hole motion in Euclidean space as a diffusion process
• Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
• Harmonic oscillator chain in noncommutative phase space with rotational symmetry
• Spectra of disc operator for twisted acceleration-enlarged Newton-Hooke space-times
• Snyder and their representation with creation and annihilation operators
• On black hole spectroscopy via quantum tunneling