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Noncommutative spherically symmetric spaces

Seán Murray^*

Jan Govaerts^†

Centre for Cosmology, Particle Physics and Phenomenology, Université catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium

Centre for Cosmology, Particle Physics and Phenomenology, Université catholique de Louvain, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium and International Chair in Mathematical Physics and Applications, University of Abomey-Calavi, 072 B. P. 50, Cotonou, Republic of Benin

^*sean.murray@uclouvain.be
^†jan.govaerts@uclouvain.be; Fellow of the Stellenbosch Institute for Advanced Study (STIAS), 7600 Stellenbosch, South Africa.

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Phys. Rev. D 83, 025009 – Published 10 January, 2011

DOI: https://doi.org/10.1103/PhysRevD.83.025009

Abstract

We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder’s noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.

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References (45)

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