PoS - Proceedings of Science
Volume 412 - RDP online PhD school and workshop "Aspects of Symmetry" (Regio2021) - Session 2
Supersymmetric extensions of oscillator- and Coulomb-like systems
E.Β Khastyan
Full text: pdf
Published on: May 16, 2022
We suggest the 𝑠𝑒(1, 𝑁|𝑀)-superconformal mechanics formulated in terms of phase superspace
given by the non-compact analog of complex projective superspace CP𝑁|𝑀. We parameterized this
phase space by the specific coordinates allowing us to interpret it as a higher-dimensional super-analog
of the Lobachevsky plane parameterized by lower half-plane (Klein model). Then we transited to
the canonical coordinates corresponding to the known separation of the "radial" and "angular" parts
of (super)conformal mechanics. Relating the "angular" coordinates with action-angle variables we
demonstrated that the proposed scheme allows constructing the 𝑠𝑒(1, 𝑁|𝑀) superconformal extensions
of a wide class of superintegrable systems. We also proposed the superintegrable oscillator-like
system with a 𝑠𝑒(1, 𝑁|𝑀) dynamical superalgebra, and found that it admits deformed N = 2𝑀
PoincarΓ© supersymmetry.
DOI: https://doi.org/10.22323/1.412.0010
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