Euler top and freedom in supersymmetrization of one-dimensional mechanics

TL;DR

This paper develops a supersymmetrization scheme for one-dimensional mechanical systems, including the Euler top, using complex projective space, resulting in a family of integrable N=2k supersymmetric Hamiltonians parameterized by arbitrary functions.

Contribution

It introduces a novel supersymmetrization approach for one-dimensional systems on complex projective space, expanding the class of integrable supersymmetric models.

Findings

Constructed a supersymmetrization scheme for systems with positive Hamiltonian.

Produced a family of N=2k supersymmetric Hamiltonians with arbitrary parameters.

Extended the supersymmetrization of the Euler top within this framework.

Abstract

Recently A.Galajinsky has suggested the N=1 supersymmetric extension of Euler top and made a few interesting observations on its properties [arXiv:2111.06083 [hep-th]]. In this paper we use the formulation of the Euler top as a system on complex projective plane, playing the role of phase space, i.e. as a one-dimensional mechanical system. Then we suggest the supersymmetrization scheme of the generic one-dimensional systems with positive Hamiltonian which yields a priori integrable family of N=2k supersymmetric Hamiltonians parameterized by N/2 arbitrary real functions.