Abstract
We use Berezin's dequantization procedure to define a formal *-product on the algebra of smooth functions on the unit disk in ℂ. We prove that this formal *-product is convergent on a dense subalgebra of the algebra of smooth functions.
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References
Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D., Deformation theory and quantization,Lett. Math. Phys. 1, 521–530 (1977).
Bayen, F., Flato, M., Fronsdal, C., Lichnerowicz, A., and Sternheimer, D., Deformation theory and quantization,Ann. Phys. 111, 61–110 (1978).
Berezin, F. A., Quantisation of Kähler manifold,Comm. Math. Phys. 40, 153 (1975).
Cahen, M., Gutt, S., and Rawnsley, J., Quantization of Kähler manifolds I: geometric interpretation of Berezin's quantisation,J. Geom. Phys. 7, 45–62 (1990).
Cahen, M., Gutt, S., and Rawnsley, J., Quantization of Kähler manifolds. II,Trans. Amer. Math. Soc. 337, 73–98 (1993).
Combet, E.,Intégrales exponentielles., Lecture Notes in Mathematics 937, Springer-Verlag, Berlin, Heidelberg, New York, 1982.
Moreno, C.,* products onD 1(ℂ,S 2) and related spectral analysis,Lett. Math. Phys. 7, 181–193 (1983).
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Cahen, M., Gutt, S. & Rawnsley, J. Quantization of Kähler manifolds. III. Lett Math Phys 30, 291–305 (1994). https://doi.org/10.1007/BF00751065
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DOI: https://doi.org/10.1007/BF00751065