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arXiv · 2107.05832

Snyder and their representation with creation and annihilation operators

Juan M. Romero·Leonardo Ortíz
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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.

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Juan M. Romero, Leonardo Ortíz. 2021-07-13. Snyder and their representation with creation and annihilation operators. https://arxiv.org/abs/2107.05832

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