Snyder and their representation with creation and annihilation operators

Abstract

Inspired by the Schwinger's representation of angular momentum, we propose a representation of certain operators where we use the algebra of the annihilation and creation operators. In particular, we propose a representation of the Snyder space-time with the help of the annihilation and creation operators, which create and annihilate quantum of space. In addition, we show that by using a matrix representation of the $SO(3)$ or $SU(2)$ Lie algebra it is possible to obtain a representation of the spacial sector of Snyder space-time. Finally, we obtain a quantized expectation value of the area of a sphere.

12 pages, non figures

References in corpus (6)

• Conformal Invariance in noncommutative geometry and mutually interacting Snyder Particles
• Discreteness of area in noncommutative space
• Spacetime singularity resolution in Snyder noncommutative space
• Snyder dynamics in a Schwarzschild spacetime
• The Area Quantum and Snyder Space
• Snyder-de Sitter model from two-time physics