Symmetries in superintegrable deformations of oscillator and Coulomb systems: Holomorphic factorization

Abstract

We propose a unified description for the constants of motion for superintegrable deformations of the oscillator and Coulomb systems on N -dimensional Euclidean space, sphere and hyperboloid. We also consider the duality between these generalized systems and present some example.

Supersymmetric hyperbolic Calogero-Sutherland models by gauging

“…For simplicity, we put a = −b = 1 . We also introduce the new fields 47) and, in what follows, omit the primes on the newly defined fields. The bosonic part of the action (4.46) becomes…”

“…For supersymmetric many-particle generalizations of the Pöschl-Teller system see, e.g.,[45,46,47,48,49].…”

Non-compact Complex Projective Superspaces by Hamiltonian reduction

“…In the series of papers ( [8][9][10][11]) so called Calogero-Oscillator and Calogero-Coulomb systems had been studied in spherical coordinates and by the use of compex coordinates an intresting results were obtained.…”

Superintegrable deformations of oscillator and Coulomb systems

“…In Section 1. 3 We focus on the Hamiltonian approach for the supersymmetric classical mechanics, since the last chapter of this thesis is devoted to that subject.…”

“…The second chapter of this thesis is based on the three articles [1,2,3]. The material of the third chapter can be found in [4].…”