Superspace formulation of N=2 pseudomechanics and superpotentials

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Abstract
The general formalism of N=2 pseudomechanics in the superspace is presented for one spatial dimension. Taking into account the (super) symmetries of the Lagrangian, an exhaustive classification of superpotentials into three categories is obtained. The first class contains the harmonic oscillator potential, the free particle constant potential, and the superposition of both with a linear potential. The second one contains the λ2/q2 potential and its superposition with the harmonic oscillator potential and a constant one. The third class contains all other potentials. Through Noether’s theorem, conserved quantities are associated with (super)symmetry properties, and, for each class, we, respectively, get the following superalgebras: osp(2,2) ⧠ sh(1), osp(2,2), and spl(1,1) ⧠ so(2).

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