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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), harmonic oscillator (HO) and inverted harmonic oscillator (IHO) as parabolic, elliptic and hyperbolic realizations of one conformal/metaplectic str…
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…
hep-th2023★ 4 cited
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…