Quantization of Length in Spaces with Position-Dependent Noncommutativity

Abstract

We present a novel approach to quantizing the length in noncommutative spaces with positional-dependent noncommutativity. The method involves constructing ladder operators that change the length not only along a plane but also along the third direction due to a noncommutative parameter that is a combination of canonical/Weyl-Moyal type and Lie algebraic type. The primary quantization of length in canonical-type noncommutative space takes place only on a plane, while in the present case, it happens in all three directions. We establish an operator algebra that allows for the raising or lowering of eigenvalues of the operator corresponding to the square of the length. We also attempt to determine how the obtained ladder operators act on different states and work out the eigenvalues of the square of the length operator in terms of eigenvalues corresponding to the ladder operators. We conclude by discussing the results obtained.

14 pages, 1 figure

References in corpus (11)

• A Gravity Theory on Noncommutative Spaces
• Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
• Noncommutative Gravity
• Lie algebraic Noncommutative Gravity
• Position-dependent noncommutativity in quantum mechanics
• Quanta of Geometry: Noncommutative Aspects
• Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves
• Noncommutative Two Dimensional Gravities
• Particle phenomenology on noncommutative spacetime
• Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
• On the Quantization of Length in Noncommutative Spaces