Tuynman, G. M. Quantization: Towards a comparison between methods. (English) Zbl 0639.58035 J. Math. Phys. 28, 2829-2840 (1987). In this paper it is shown that the procedure of geometric quantization applied to Kähler manifolds gives the following result: the Hilbert space \({\mathcal H}\) consists, roughly speaking, of holomorphic functions on the phase space M and to each classical observable f (i.e., a real function on M) is associated an operator \({\mathfrak f}\) on \({\mathcal H}\) as follows: first multiply by \(f+1/4\hslash \Delta_{dR}f\) \((\Delta_{dR}\) being the Laplace-de Rham operator on the Kähler manifold M) and then take the holomorphic part. Cited in 15 Documents MSC: 58Z05 Applications of global analysis to the sciences 53D50 Geometric quantization 81S10 Geometry and quantization, symplectic methods Keywords:geometric quantization applied to Kähler manifolds; Laplace-de Rham operator PDFBibTeX XMLCite \textit{G. M. Tuynman}, J. Math. Phys. 28, 2829--2840 (1987; Zbl 0639.58035) Full Text: DOI References: [1] DOI: 10.1063/1.527642 · Zbl 0616.58041 · doi:10.1063/1.527642 [2] DOI: 10.1070/IM1974v008n05ABEH002140 · Zbl 0312.53049 · doi:10.1070/IM1974v008n05ABEH002140 [3] DOI: 10.1007/BF01609397 · Zbl 1272.53082 · doi:10.1007/BF01609397 [4] DOI: 10.1016/0393-0440(86)90015-X · Zbl 0615.58024 · doi:10.1016/0393-0440(86)90015-X [5] DOI: 10.1070/IM1975v009n02ABEH001480 · Zbl 0324.53049 · doi:10.1070/IM1975v009n02ABEH001480 [6] Moreno C., Ann. Isnt. H. Poincare Sec. A 38 pp 215– (1983) [7] DOI: 10.1007/BF00574162 · Zbl 0618.53049 · doi:10.1007/BF00574162 [8] DOI: 10.1007/BF00416512 · Zbl 0681.53036 · doi:10.1007/BF00416512 [9] DOI: 10.1007/BF00400432 · Zbl 0528.58014 · doi:10.1007/BF00400432 [10] DOI: 10.2307/2374055 · Zbl 0506.22018 · doi:10.2307/2374055 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.