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Quantum mechanics as a deformation of classical mechanics |
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| Authors: | Bayen F. Flato M. Fronsdal C. Lichnerowicz A. Sternheimer D. |
| Affiliation: | (1) Département de Mathématiques, Université de Paris 6, 75230 Paris Cedex 05, France;(2) University of California, 90024 Los Angeles, Calif., USA;(3) Present address: Physique Mathématique, Collège de France, France;(4) Université de Dijon, 21000 Dijon, France;(5) Collège de France, 75231 Paris Cedex 05, France |
| Abstract: | Mathematical properties of deformations of the Poisson Lie algebra and of the associative algebra of functions on a symplectic manifold are given. The suggestion to develop quantum mechanics in terms of these deformations is confronted with the mathematical structure of the latter. As examples, spectral properties of the harmonic oscillator and of the hydrogen atom are derived within the new formulation. Further mathematical generalizations and physical applications are proposed.Work supported in part by the National Science Foundation. |
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