1997/02/01 by H. Kleinert, Hagen Kleinert, Sergei V. Shabanov · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cold Atom Physics and Bose-Einstein Condensates #Noncommutative and Quantum Gravity Theories #quant-ph
paper · pdf · doi:10.1016/s0375-9601(97)00410-6
published as Phys.Lett. A232 (1997) 327-332 · Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re253/preprint.html
arxiv created 1997/02/01 · openalex publication_date 1997/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that an unambiguous and correct quantization of the second-class constrained system of a free particle on a sphere in D dimensions is possible only by converting the constraints to abelian gauge constraints, which are of first class in Dirac's classification scheme. The energy spectrum is equal to that of a pure Laplace-Beltrami operator with no additional constant arising from the curvature of the sphere. A quantization of Dirac's modified Poisson brackets for second-class constraints is also possible and unique, but must be rejected since the resulting energy spectrum is physically incorrect.