Quantum mechanics model on a Kähler conifold

Stefano Bellucci; Armen Nersessian; Armen Yeranyan

doi:10.1103/PhysRevD.70.045006

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Quantum mechanics model on a Kähler conifold

Stefano Bellucci¹, Armen Nersessian^2,3, and Armen Yeranyan²

¹INFN-Laboratori Nazionali di Frascati, P.O. Box 13, I-00044, Italy
²Yerevan State University, Alex Manoogian St., 1, Yerevan 375025, Armenia
³Yerevan Physics Institute, Alikhanian Brothers St., 2, Yerevan 375036, Armenia

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Phys. Rev. D 70, 045006 – Published 17 August, 2004

DOI: https://doi.org/10.1103/PhysRevD.70.045006

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 nonconstant 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 nontrivial 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.

References (11)

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[c1] P.W. Higgs, J. Phys. A 12, 309 (1979); ibid.H.I. Leemon, 12, 489 (1979).

[c2] B. Zumino, Phys. Lett. 87B, 203 (1979); M.J. Bowick and S.G. Rajeev, Phys. Rev. Lett. 58, 535 (1987); ibid.58, 1158(E) (1987).

[c3] D.V. Fursaev and S.N. Solodukhin, Phys. Rev. D 52, 2133 (1995); A. Strominger, Nucl. Phys. B451, 96 (1995); C. Mayer and T. Mohaupt, Class. Quantum Grav. 21, 1879 (2004).

[c4] S. Bellucci and A. Nersessian, Phys. Rev. D 67, 065013 (2003).

[c5] A. Nersessian and A. Yeranyan, J. Phys. A 37, 2791 (2004).

[c6] D. Zwanziger, Phys. Rev. 176, 1480 (1968); H.V. McIntosh and A. Cisneros, J. Math. Phys. 11, 896 (1970).

[c7] A. Nersessian and G. Pogosyan, Phys. Rev. A 63, 020103(R) (2001).

[c8] A. Nersessian, V. Ter-Antonyan, and M.M. Tsulaia, Mod. Phys. Lett. A 11, 1605 (1996).

[c9] S.C. Zhang and J.P. Hu, Science 294, 823 (2001); D. Karabali and V.P. Nair, Nucl. Phys. B641, 533 (2002); B.A. Bernevig, J.P. Hu, N. Toumbas, and S.C. Zhang, Phys. Rev. Lett. 91, 236803 (2003).

[c10] E.G. Kalnins, W. Miller, Jr., and G.S. Pogosyan, J. Math. Phys. 41, 2629 (2000).

[c11] D. McMullan and J. Paterson, J. Math. Phys. 30, 477 (1989); ibid.30, 487 (1989).

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Quantum mechanics model on a Kähler conifold

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