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Rotation invariance of quantum Laplacians

In this paper, we prove that the quantum Gross Laplacian and the quantum Beltrami Laplacian denoted, respectively, as and are rotation-invariant operators. For this purpose, we use the Schwartz–Grothendieck kernel theorem and the characterization theorem of rotation-invariant distributions and operators. Then, we give a characterization of all quantum operators by means of rotation invariance.