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Springer eBooks

Geometric quantization of the Kepler problem with a magnetic charge

Vassil V. Tsanov, Ivaïlo M. Mladenov

Published Oct 29, 2005• 6 citations
Publisher
DOI
10.1007/bfb0012288

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In the presence of a magnetic field, the Maslov quantization condition is not available in the original form. An alternative quantization condition is proposed with the aid of a principal U(1) bundle over a phase space and a connection whose curvature form is the charged symplectic form. By means of this quantization condition, quasiclassical eigenvalues of the Kepler problem with a centrifugal potential and Dirac’s monopole field are calculated, which turn out to coincide with the eigenvalues of the quantized problem.