×

Deformation theory and quantization. I: Deformations of symplectic structures. (English) Zbl 0377.53024


MSC:

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

Citations:

Zbl 0377.53025
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Wigner, E. P., Phys. Rev., 40, 749 (1932) · Zbl 0004.38201
[2] Weyl, H., Z. Phys., 46, 1 (1927)
[3] Agarwal, G. S.; Wolf, E., Phys. Rev. D, 2, 2161 (1970) · Zbl 1227.81196
[4] Chi Liu, K., J. Math. Phys., 17, 859 (1976) · Zbl 0351.46028
[5] Remler, E. A., Ann. Phys. (N.Y.), 95, 455 (1975)
[6] Flato, M.; Lichnerowicz, A.; Sternheimer, D., C. R. Acad. Sci. Paris Ser. A, 279, 877 (1974) · Zbl 0289.53031
[7] Flato, M.; Lichnerowicz, A.; Sternheimer, D., Compositio Math., 31, 47 (1975) · Zbl 0317.53039
[8] Flato, M.; Lichnerowicz, A.; Sternheimer, D., J. Math. Phys., 17, 1754 (1976)
[9] Gerstenhaber, M., Ann. Math., 79, 59 (1964) · Zbl 0123.03101
[10] Vey, J., Math. Helvet., 50, 421 (1975), Comment · Zbl 0351.53029
[11] Flato, M.; Lichnerowicz, A.; Sternheimer, D., C. R. Acad. Sci. Paris Ser. A, 283, 19 (1976) · Zbl 0346.53026
[12] Bayen, F.; Flato, M.; Fronsdal, C.; Lichnerowicz, A.; Sternheimer, D., Deformation theory and quantization. II. Physical applications, Ann. Phys. (N.Y.), 111, 111 (1978) · Zbl 0377.53025
[13] Nijenhuis, A., Indag. Math., 17, 390 (1955)
[14] A. LichnerowiczJ. Differential Geometry; A. LichnerowiczJ. Differential Geometry · Zbl 0405.53024
[15] Avez, A.; Lichnerowicz, A.; Diaz-Miranda, A., J. Differential Geometry, 9, 1 (1974)
[16] Bayen, F.; Flato, M.; Fronsdal, C.; Lichnerowicz, A.; Sternheimer, D., Lett. Math. Phys., 1, 521 (1977)
[17] Dirac, P. A.M., (Lectures on Quantum Mechanics. Lectures on Quantum Mechanics, Belfer Graduate School of Sciences Monograph Series No. 2 (1964), Yeshiva Univ: Yeshiva Univ New York) · Zbl 0141.44603
[18] Lichnerowicz, A., C. R. Acad. Sci. Paris Ser. A, 280, 523 (1976)
[19] Lichnerowicz, A., Lett. Math. Phys., 2, 2 (1977)
[20] Souriau, J. M., Structures des Systèmes Dynamiques (1970), Dunod: Dunod Paris, This map was introduced by · Zbl 0186.58001
[21] Dixmier, J., Algèbres Enveloppantes (1974), Gauthier-Villars: Gauthier-Villars Paris, For information about enveloping algebras, see · Zbl 0308.17007
[22] Vergne, M., Bull. Soc. Math. France, 100, 301 (1972) · Zbl 0256.17002
[23] Bourbaki, N., Algèbre (1970), Hermann: Hermann Paris, Chap. II, Sect. 1, No. 13, 3rd ed., 1962 or new edition · Zbl 0211.02401
[24] Hochschild, G., The Structure of Lie Groups (1966) · Zbl 0149.27603
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.