Shifted Poisson structures and deformation quantization
نویسندگان
چکیده
منابع مشابه
Poisson Sigma Models and Deformation Quantization
This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplectic groupoid), explaining in particular the classical origin of the non-commutativity of the strin...
متن کاملDeformation Quantization of Pseudo Symplectic(Poisson) Groupoids
We introduce a new kind of groupoid—a pseudo étale groupoid, which provides many interesting examples of noncommutative Poisson algebras as defined by Block, Getzler, and Xu. Following the idea that symplectic and Poisson geometries are the semiclassical limits of the corresponding quantum geometries, we quantize these noncommutative Poisson manifolds in the framework of deformation quantizatio...
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 کاملOn quantization of quadratic Poisson structures
Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel’d [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.
متن کاملDeformation quantization of Poisson manifolds in the derivative expansion
Deformation quantization of Poisson manifolds is studied within the framework of an expansion in powers of derivatives of Poisson structures. Using the Lie group associated with a Poisson bracket algebra we find a solution to the associativity equation in the leading and next-to-leading orders in this expansion.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Topology
سال: 2017
ISSN: 1753-8416,1753-8424
DOI: 10.1112/topo.12012