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Publications Influence

Quantum mechanics as a deformation of classical mechanics

- F. Bayen, M. Flato, C. Frønsdal, A. Lichnerowicz, D. Sternheimer
- Mathematics
- 1 June 1977

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… Expand

211 12

Deformation theory and quantization. I. Deformations of symplectic structures

- F. Bayen, M. Flato, C. Frønsdal, A. Lichnerowicz, D. Sternheimer
- Physics
- 1 March 1978

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 Poisson… Expand

1,204 10

Closed star products and cyclic cohomology

- A. Connes, M. Flato, D. Sternheimer
- Mathematics
- 1992

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 a… Expand

125 9

Deformation quantization: Twenty years after

- D. Sternheimer
- Mathematics, Physics
- 10 September 1998

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 of… Expand

122 6- PDF

Massless Particles, Conformal Group and De Sitter Universe

- E. Angelopoulos, M. Flato, C. Frønsdal, D. Sternheimer
- Physics
- 15 March 1981

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 obtain… Expand

114 4

Deformation quantization and Nambu Mechanics

- G. Dito, Moshé Flato, D. Sternheimer, L. Takhtajan
- Physics, Mathematics
- 5 February 1996

Starting from deformation quantization (star-products), the quantization problem of Nambu Mechanics is investigated. After considering some impossibilities and pushing some analogies with field… Expand

130 3- PDF

Deformation Quantization: Genesis, Developments and Metamorphoses

- G. Dito, D. Sternheimer
- Mathematics, Physics
- 18 January 2002

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 indicate… Expand

184 3- PDF

Deformation theory applied to quantization and statistical mechanics

- H. Basart, M. Flato, A. Lichnerowicz, D. Sternheimer
- Mathematics
- 1 November 1984

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 classical… Expand

53 2

Deformation theory and quantization. II. Physical applications

- F. Bayen, M. Flato, C. Frønsdal, A. Lichnerowicz, D. Sternheimer
- Physics
- 1 March 1978

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 of… Expand

578 1

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