Projective geometry and Cayley transformations provide a common framework for the free particle-oscillator correspondences via the Schwarzian cocycle.
Weak-strong duality of the non-commutative Landau problem in- duced by a two-vortex permutation, and conformal bridge transformation,
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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.