dorsal/arxiv
View SchemaProper Dirac Quantization of Free Particle on D-Dimensional Sphere
| Authors | Hagen Kleinert, Sergei V. Shabanov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9702006 |
| URL | https://arxiv.org/abs/quant-ph/9702006 |
| DOI | 10.1016/S0375-9601(97)00410-6 |
| Journal | Phys.Lett. A232 (1997) 327-332 |
Abstract
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.
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"abstract": "We show that an unambiguous and correct quantization of the second-class\nconstrained system of a free particle on a sphere in $D$ dimensions is possible\nonly by converting the constraints to abelian gauge constraints, which are of\nfirst class in Dirac\u0027s classification scheme. The energy spectrum is equal to\nthat of a pure Laplace-Beltrami operator with no additional constant arising\nfrom the curvature of the sphere. A quantization of Dirac\u0027s modified Poisson\nbrackets for second-class constraints is also possible and unique, but must be\nrejected since the resulting energy spectrum is physically incorrect.",
"arxiv_id": "quant-ph/9702006",
"authors": [
"Hagen Kleinert",
"Sergei V. Shabanov"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/S0375-9601(97)00410-6",
"journal_ref": "Phys.Lett. A232 (1997) 327-332",
"title": "Proper Dirac Quantization of Free Particle on D-Dimensional Sphere",
"url": "https://arxiv.org/abs/quant-ph/9702006"
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