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Quantum mechanics as a deformation of classical mechanics
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 termsExpand
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Deformation theory and quantization. I. Deformations of symplectic structures
Abstract We present a mathematical study of the differentiable deformations of the algebras associated with phase space. Deformations of the Lie algebra of C∞ functions, defined by the PoissonExpand
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Closed star products and cyclic cohomology
We define the notion of a closed star product. A (generalized) star product (deformation of the associative product of functions on a symplectic manifold W) is closed iff integration over W is aExpand
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Deformation quantization: Twenty years after
We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth ofExpand
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Massless Particles, Conformal Group and De Sitter Universe
We first review a recent result on the uniqueness of the extension to the conformal group of massless representations of the Poincare group. By restricting these representations to SO(3,2) we obtainExpand
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Deformation quantization and Nambu Mechanics
Starting from deformation quantization (star-products), the quantization problem of Nambu Mechanics is investigated. After considering some impossibilities and pushing some analogies with fieldExpand
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Deformation Quantization: Genesis, Developments and Metamorphoses
We start with a short exposition of developments in physics and mathematics that preceded, formed the basis for, or accompanied, the birth of deformation quantization in the seventies. We indicateExpand
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Deformation theory applied to quantization and statistical mechanics
After a review of the deformation (star product) approach to quantization, treated in an autonomous manner as a deformation (with parameter ħ) of the algebraic composition law of classicalExpand
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Deformation theory and quantization. II. Physical applications
Abstract In the preceding paper general deformations of the structures based on the classical symplectic manifolds were examined. Quantization can be understood as a deformation of the algebra ofExpand
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