The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
Integrability in Perturbed Black Holes: Background Hidden Structures
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A self-dual curvature formulation unifies the Regge-Wheeler-Zerilli and Bardeen-Press-Teukolsky equations on spherical backgrounds as components of one tensorial curvature equation.
Projective geometry and Cayley transformations provide a common framework for the free particle-oscillator correspondences via the Schwarzian cocycle.
citing papers explorer
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The Free Particle--Oscillator--Inverted Oscillator Triangle: Conformal Bridges, Metaplectic Rotations and $\mathfrak{osp}(1|2)$ Structure
The free particle, harmonic oscillator, and inverted oscillator are unified as parabolic, elliptic, and hyperbolic realizations of the same conformal module, with explicit mappings between their states, coherent states, and scattering data via metaplectic rotations and Mellin transforms.
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Unifying the Regge-Wheeler-Zerilli and Bardeen-Press-Teukolsky formalisms on spherical backgrounds
A self-dual curvature formulation unifies the Regge-Wheeler-Zerilli and Bardeen-Press-Teukolsky equations on spherical backgrounds as components of one tensorial curvature equation.
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Projective Time, Cayley Transformations and the Schwarzian Geometry of the Free Particle--Oscillator Correspondence
Projective geometry and Cayley transformations provide a common framework for the free particle-oscillator correspondences via the Schwarzian cocycle.