Proper Dirac quantization of a free particle on a D-dimensional sphere

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...

Full description

Saved in:
Bibliographic Details
Published in:Physics letters. A 1997-08, Vol.232 (5), p.327-332
Main Authors: Kleinert, Hagen, Shabanov, Sergei V.
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0375-9601
1873-2429
DOI:10.1016/S0375-9601(97)00410-6