5 papers
Affine Extension of the Free-Particle--Oscillator--Inverted-Oscillator Triangle
Andrey Alcala, Mikhail S. Plyushchay
We study the one-dimensional linear-potential system as an affine extension of the conformal triangle formed by the free particle, harmonic oscillator (HO) and inverted harmonic os…
Morse Bridge between Planar Kepler and Hyperbolic Landau Dynamics
Mikhail S. Plyushchay
We show that two paradigmatic systems, the planar Kepler--Coulomb problem and the Landau problem on the hyperbolic plane , are connected by a common one-dimensional mediator:…
The Free Particle--Oscillator--Inverted Oscillator Triangle: Conformal Bridges, Metaplectic Rotations and Structure
Andrey Alcala, Mikhail S. Plyushchay
We study the free particle (FP), the harmonic oscillator (HO) and the inverted harmonic oscillator (IHO) as parabolic, elliptic and hyperbolic realizations of one conformal/metaple…
Projective Time, Cayley Transformations and the Schwarzian Geometry of the Free Particle--Oscillator Correspondence
Andrey Alcala, Mikhail S. Plyushchay
We investigate the relation between the one--dimensional free particle and the harmonic oscillator from a unified viewpoint based on projective geometry, Cayley transformations, an…
Conformal Symmetry of Relativistic and Nonrelativistic Systems and AdS/CFT Correspondence
Carlos Leiva, Mikhail S. Plyushchay
The nonlinear realization of conformal so(2,d) symmetry for relativistic systems and the dynamical conformal so(2,1) symmetry of nonrelativistic systems are investigated in the con…