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0863.58030
Gotay,
M.J.; Grundling,
H.B.; Tuynman,
G.M.
Obstruction results in quantization theory. (English)
[J] J.
Nonlinear Sci. 6, No.5, 469-498 (1996). [ISSN 0938-8974]
It is well-known that fifty years ago Groenewold and van Hove have discovered
obstructions to quantizations. Their no -- go theorems assert that it is
impossible to consistently quantize every classical observable on the phase
space $\bbfR^{2n}$. A similar obstruction was recently found by Gotay for
$S^2$, buttressing up the common belief that no -- go theorems should hold
in some generality. Surprisingly enough this is not so -- recently Gotay
has proven that there is no obstruction to quantizing a torus.\par In the
paper under review the authors take first steps towards delineating the
circumstances under which such obstructions will appear and understanding
the mechanisms which produce them. Their objectives are to conjecture a
generalized Groenewald -- van Hove theorem and to determine the maximal
subalgebras of observables which can be consistently quantized. Their discussion
is independent of any particular method of quantization. In conclusion a
very nice paper.
[ M.Puta
(Timisoara) ]
Keywords: obstructions; van Hove theorem; observables; quantization