Bayen, F.; Flato, Moshé; Frønsdal, Christian; Lichnerowicz, A.; Sternheimer, D. Deformation theory and quantization. I: Deformations of symplectic structures. (English) Zbl 0377.53024 Ann. Phys. 111, 61-110 (1978). Reviewer: A. Crumeyrolle Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 43 ReviewsCited in 445 Documents MSC: 53D55 Deformation quantization, star products 53D05 Symplectic manifolds (general theory) 81S10 Geometry and quantization, symplectic methods Keywords:deformation quantization Citations:Zbl 0377.53025 PDF BibTeX XML Cite \textit{F. Bayen} et al., Ann. Phys. 111, 61--110 (1978; Zbl 0377.53024) Full Text: DOI References: [1] Wigner, E. P., Phys. Rev., 40, 749 (1932) [2] Weyl, H., Z. Phys., 46, 1 (1927) · JFM 53.0848.02 [3] Agarwal, G. S.; Wolf, E., Phys. Rev. D, 2, 2161 (1970) [4] Chi Liu, K., J. Math. Phys., 17, 859 (1976) [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) [7] Flato, M.; Lichnerowicz, A.; Sternheimer, D., Compositio Math., 31, 47 (1975) [8] Flato, M.; Lichnerowicz, A.; Sternheimer, D., J. Math. Phys., 17, 1754 (1976) [9] Gerstenhaber, M., Ann. Math., 79, 59 (1964) [10] Vey, J., Math. Helvet., 50, 421 (1975), Comment [11] Flato, M.; Lichnerowicz, A.; Sternheimer, D., C. R. Acad. Sci. Paris Ser. A, 283, 19 (1976) [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) [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) [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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.