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arXiv · 2111.07391

Laplacian on fuzzy de Sitter space

Bojana Brkic·Maja Buric·Dusko Latas
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Abstract

We study details of geometry of noncommutative de Sitter space: we determine the Riemann and Ricci curvature tensors, the energy and the Laplacian. We find, in particular, that fuzzy de Sitter space is an Einstein space, $R_{ab}=-3\zeta\,\eta_{ab}$. The Laplacian, defined in the noncommutative frame formalism, is not hermitian and gives nonunitary evolution. When symmetrically ordered, it has the usual quadratic form $\Delta=\Pi_a\Pi^a$ (when acting on functions in representation space, $\Psi\in {\cal H}$): we find its eigenstates and discuss its spectrum. This result is a first step in a study of the scalar field Laplacian, $\Delta = [\Pi_a, [\Pi^a,\ ]]$, and its propagator.

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Bojana Brkic, Maja Buric, Dusko Latas. 2021-11-14. Laplacian on fuzzy de Sitter space. https://doi.org/10.1088/1361-6382%2Fac6133

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