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Title:
Proper Dirac Quantization of Free Particle on
D-Dimensional Sphere
Authors:
Hagen KLEINERT and Sergei V. SHABANOV
Comment: 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
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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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