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Bayen, F.; Flato, Moshé; Frønsdal, Christian; Lichnerowicz, A.; Sternheimer, D.

Deformation theory and quantization. II: Physical applications. (English) Zbl 0377.53025

Ann. Phys. 111, 111-151 (1978).
Reviewer: A. Crumeyrolle
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Cited in 28 Reviews
Cited in 213 Documents

MSC:

53D55 Deformation quantization, star products
53D05 Symplectic manifolds (general theory)
81S10 Geometry and quantization, symplectic methods

Citations:

Zbl 0377.53024
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\textit{F. Bayen} et al., Ann. Phys. 111, 111--151 (1978; Zbl 0377.53025)
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References:

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[3] Bayen, F.; Flato, M.; Fronsdal, C.; Lichnerowicz, A.; Sternheimer, D., Deformation theory and quantization. I. deformations of symplectic structures, Ann. phys. (N.Y.), 111, 61, (1978), henceforth referred to as I · Zbl 0377.53024
[4] Weyl, H., The theory of groups and quantum mechanics, (1931), Dover New York · JFM 58.1374.01
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[10] The map J is Souriau’s “moment”
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[14] Martin, C., Lett. math. phys., 1, 155, (1976), See
[15] Flato, M.; Lichnerowicz, A.; Sternheimer, D., J. math. phys., 17, 1754, (1976)
[16] Segal, I.E., (), 99-117, and earlier references quoted therein
[17] Agarwal, G.S.; Wolf, E.; Agarwal, G.S.; Wolf, E., Phys. rev. D, Phys. rev. D, 2, 2206, (1970), One simply substitutes in (2-4) formal powers of the field-theoretical Poisson bracket (using higher-order functional derivatives). This has of course to be justified. See also · Zbl 1227.81198
[18] {\scE. Remler}, preprint, College of William and Mary, 1977.
[19] Guenin, M.; Flato, M.M.; Guenin, M., Phys. lett., Helv. phys. acta, 50, 117, (1977), Ref. 8
[20] {\scR. Casalbuoni}, CERN preprint TH. 2139 (March 1976). {\scK. Drühl}, Max-Planck-Institute preprint, Starnberg, December 1976. {\scA. Sudbery}, Univ. of York preprint, October 1975.
[21] Gervais, J.L.; Sakita, B., Nucl. phys. B, 34, (1971)
[22] Wess, J.; Zumino, B.; Schwinger, J.; Schwinger, J.; Flato, M.; Hillion, P., (), Phys. rev. D, 1, 1667, (1970), See also
[23] ()
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