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Quantum Mechanics Model on Kähler conifold

Stefano Bellucci·Armen Nersessian·Armen Yeranyan
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Abstract

We propose an exactly-solvable model of the quantum oscillator on the class of Kähler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum number, when the space has non-constant curvature. We reduce the model to a three-dimensional system interacting with the Dirac monopole. Owing to noncommutativity of the reduction and quantization procedures, the Hamiltonian of the reduced system gets non-trivial quantum corrections. We transform the reduced system into a MIC-Kepler-like one and find that quantum corrections arise only in its energy and coupling constant. We present the exact spectrum of the generalized MIC-Kepler system. The one-(complex) dimensional analog of the suggested model is formulated on the Riemann surface over the complex projective plane and could be interpreted as a system with fractional spin.

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Stefano Bellucci, Armen Nersessian, Armen Yeranyan. 2004-06-18. Quantum Mechanics Model on Kähler conifold. https://doi.org/10.1103/physrevd.70.045006

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