Book Review: Nonlinear Poisson brackets, geometry and quantization
نویسندگان
چکیده
منابع مشابه
On the quantization of Poisson brackets
In this paper we introduce two classes of Poisson brackets on algebras (or on sheaves of algebras). We call them locally free and nonsingular Poisson brackets. Using the Fedosov’s method we prove that any locally free nonsingular Poisson bracket can be quantized. In particular, it follows from this that all Poisson brackets on an arbitrary field of characteristic zero can be quantized. The well...
متن کاملAn operadic approach to deformation quantization of compatible Poisson brackets
An analogue of the Livernet–Loday operad for two compatible brackets, which is a flat deformation of the bi-Hamiltonian operad is constructed. The Livernet–Loday operad can be used to define ⋆-products and deformation quantization for Poisson structures. The constructed operad is used in the same way, introducing a definition of operadic deformation quantization of compatible Poisson structures...
متن کاملR-commutative Geometry and Quantization of Poisson Algebras
An r-commutative algebra is an algebra A equipped with a Yang-Baxter operator R:A ⊗ A → A ⊗ A satisfying m = mR, where m:A ⊗ A → A is the multiplication map, together with the compatibility conditions R(a⊗ 1) = 1 ⊗ a, R(1 ⊗ a) = a ⊗ 1, R(id ⊗m) = (m ⊗ id)R2R1 and R(m ⊗ id) = (id ⊗ m)R1R2. The basic notions of differential geometry extend from commutative (or supercommutative) algebras to r-comm...
متن کاملPoisson geometry and deformation quantization near a strictly pseudoconvex boundary
Let X be a complex manifold with strongly pseudoconvex boundary M . If ψ is a defining function for M , then − logψ is plurisubharmonic on a neighborhood of M in X, and the (real) 2-form σ = i∂∂(− logψ) is a symplectic structure on the complement of M in a neighborhood in X of M ; it blows up along M . The Poisson structure obtained by inverting σ extends smoothly across M and determines a cont...
متن کاملLinearization of Poisson Brackets
We review the linearization of Poisson brackets and related problems, in the formal, analytic and smooth categories.
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1996
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-96-00619-2