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.
Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons
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Extra spin-2 in quadratic gravity is a dual inverted harmonic oscillator with vanishing Källén–Lehmann density, fixing a principal-value propagator and preserving unitarity with renormalizability.
The inverted harmonic oscillator and its dual are argued to underpin a unique unitary renormalizable quantum gravity in four dimensions, yielding a non-singular universe and Starobinsky inflation.
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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Unitary Quadratic Quantum Gravity in 4D
Extra spin-2 in quadratic gravity is a dual inverted harmonic oscillator with vanishing Källén–Lehmann density, fixing a principal-value propagator and preserving unitarity with renormalizability.
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The Saddle Point of Everything
The inverted harmonic oscillator and its dual are argued to underpin a unique unitary renormalizable quantum gravity in four dimensions, yielding a non-singular universe and Starobinsky inflation.