172 citations · 3.5k across the 115 of their papers we have counts for
115 papers
Projective geometry of second-order supersymmetry
Stevan Cebrian, Mikhail S. Plyushchay
We show that anomaly-free second-order supersymmetry (SUSY) in quantum mechanics admits a projective-geometric formulation in terms of a projective connection and a vector field pr…
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
A common Morse Hamiltonian bridges the planar Kepler--Coulomb and hyperbolic Landau systems, linking flat electric dynamics to curved magnetic dynamics. A radial Liouville transfor…
The Free Particle--Oscillator--Inverted Oscillator Triangle: Conformal Bridges, Metaplectic Rotations and Structure
Andrey Alcala, Mikhail S. Plyushchay
We study the free particle (FP), harmonic oscillator (HO) and inverted harmonic oscillator (IHO) as parabolic, elliptic and hyperbolic realizations of one conformal/metaplectic str…
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…
Weak-strong duality of the non-commutative Landau problem induced by a two-vortex permutation, and conformal bridge transformation
Andrey Alcala, Mikhail S. Plyushchay
A correspondence is established between the dynamics of the two-vortex system and the non-commutative Landau problem (NCLP) in its sub- (non-chiral), super- (chiral) and critical p…