Lobachevsky geometry of (super)conformal mechanics

Abstract

We give a simple geometric explanation for the similarity transformation mapping one-dimensional conformal mechanics to free-particle system. Namely, we show that this transformation corresponds to the inversion of the Klein model of Lobachevsky space (non-compact complex projective plane). We also extend this picture to the N=2k superconformal mechanics described in terms of Lobachevsky superspace.

5 pages

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Cited by in corpus (18)

• Superconformal mechanics
• Hidden symmetries of integrable conformal mechanical systems
• Conformal mechanics in Newton-Hooke spacetime
• Remark on quantum mechanics with conformal Galilean symmetry
• Cuboctahedric Higgs oscillator from the Calogero model
• Remark on quantum mechanics with N=2 Schrodinger supersymmetry
• Symmetries in superintegrable deformations of oscillator/Coulomb systems: "holomorphic factorization"
• N=2 supersymmetric particle near extreme Kerr throat
• Nonlinear symmetries of perfectly invisible $PT$-regularized conformal and superconformal mechanics systems
• Lobachevsky geometry in TTW and PW systems
• Remarks on Multi-Dimensional Conformal Mechanics
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• The geometry of gauged (super)conformal mechanics
• $SU(1,1|N)$ superconformal mechanics with fermionic gauge symmetry
• Action-Angle Variables In Conformal Mechanics
• Noncompact ${\mathbf{CP}}^N$ as a phase space of superintegrable systems
• Superintegrable deformations of oscillator and Coulomb systems
• Euler top and freedom in supersymmetrization of one-dimensional mechanics