3 papers
math-ph2026
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…
hep-th2026
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…
hep-th2026
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…