Abstract
A pseudoclassical model describing a covariant harmonic oscillator with half-integer spin is studied. The model is obtained by applying the idea of the supersymmetric invariance to extend the harmonic-oscillator classical Lagrangian of Kalb and Van Alstine to the case of Grassmann variables. The wave equation appears as a linearization of that of the harmonic oscillator as much as for the case of the Dirac equation and the Klein-Gordon equation. The model is, in some sense, the analogous of that of Ramond for the spinning string in the case of two constituents. The mass spectrum is given by a set of linearly rising trajectories. The problem of the relativistic invariance in the quantum case is studied.
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