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0632.58020
Gotay,
Mark J.
Constraints, reduction, and quantization. (English)
[J] J.
Math. Phys. 27, 2051-2066 (1986). [ISSN 0022-2488]
For a constrained classical system it is possible to quantize both the extended
and the reduced phase space. The purpose of this paper is to determine under
what conditions and in what sense these two quantizations will be unitarily
equivalent. The specific class of constrained systems - those whose phase
spaces are cotangent bundles and whose groups act by point transformations
- is investigated. \par After discussing some generalities on the quantization
of constrained systems both the extended and reduced phase spaces are quantized.
In particular, quantization yields a representation of the symmetry algebra
g. A canonical unitary isomorphism between the two quantizations obtained
above is constructed. It is proved that it is possible to quantize invariant
polarization-preserving functions in either formalism with equivalent results.
\par Several examples and a discussion of possible generalizations of results
are presented in conclusion.
[ H.Kilp
]
Keywords: quantizations; constrained systems; reduced phase spaces; representation of the symmetry algebra