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Some ideas about quantization. (English) Zbl 0418.58011


MSC:

53D50 Geometric quantization
22D30 Induced representations for locally compact groups
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
81P05 General and philosophical questions in quantum theory
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations
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References:

[1] F. Bayen, M. Flato, C. Fronsdal, A. Lichnérowicz, and D. Sternheimer: Deformation Theory and Quantization, I and II.Annals of Physics; F. Bayen, M. Flato, C. Fronsdal, A. Lichnérowicz, and D. Sternheimer: Deformation Theory and Quantization, I and II.Annals of Physics
[2] Kostant, B., (Lecture Notes in Mathematics, 170 (1970), Springer-Verlag), 87
[3] Souriau, J.-M., Structure des systèmes dynamiques (1970), Dunod: Dunod Paris · Zbl 0186.58001
[4] Kostant, B., Proceedings of the International Congress of Mathematicians (September 1970), Nice
[5] Lichnérowicz, A., Lett. Math. Phys., 2, 133 (1977)
[6] Kirillov, A., Eléments de la Théorie des Représentations (1974), Edition Mir: Edition Mir Moscow
[7] Moyal, J. E., Proc. Cambr. Phil. Soc., 45, 99 (1949)
[8] Barut, A. O.; Fronsdal, C., Proc. Roy. Soc. A, 287, 523 (1965)
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