Euler top and freedom in supersymmetrization of one-dimensional mechanics

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.

8 pages

References in corpus (4)

• Action-angle variables for dihedral systems on the circle
• Lobachevsky geometry of (super)conformal mechanics
• Remarks on N=1 supersymmetric extension of the Euler top
• Kähler geometry for $su(1,N|M)$-superconformal mechanics