Abstract
We present the deformed (for the presence of Calogero potential terms) one-dimensional quantum oscillator with the exceptional Lie superalgebra F(4) as spectrum-generating superconformal algebra. The Hilbert space is given by a 16-ple of square-integrable functions. The energy levels are 23+n, with n = 0, 1, 2, …. The ground state is 7 times degenerate. The excited states are 8 times degenerate. The (7, 8, 8, 8, …) semi-infinite tower of states is recovered from the (7; 8; 1) supermultiplet of the N=8 worldline supersymmetry. The model is unique, up to similarity transformations, and admits an octonionic-covariant formulation which manifests itself as “quasi-nonassociativity.” This means, in particular, that the Calogero coupling constants are expressed in terms of the octonionic structure constants. The associated F(4) superconformal quantum mechanics is also presented.
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