Category of quantizations and inverse problem

@article{Sako2022CategoryOQ,
  title={Category of quantizations and inverse problem},
  author={Akifumi Sako},
  journal={Nuclear Physics B},
  year={2022}
}
  • Akifumi Sako
  • Published 18 May 2022
  • Mathematics
  • Nuclear Physics B

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SHOWING 1-10 OF 56 REFERENCES

Categorical perspective on quantization of Poisson algebra

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On the geometric quantization of Poisson manifolds

In a paper by Huebschmann [J. Reine Angew. Math. 408, 57 (1990)], the geometric quantization of Poisson manifolds appears as a particular case of the quantization of Poisson algebras. Here, this

Deformation quantization of Heisenberg manifolds

ForM a smooth manifold equipped with a Poisson bracket, we formulate aC*-algebra framework for deformation quantization, including the possibility of invariance under a Lie group of diffeomorphisms

A Generalization of the Quantization of Poisson Manifolds

We propose a unified perspective of quantization using a categorical approach. From a fixed Poisson algebra, we define quantization categories as subcategories of theR-module category equipped with

Dirac operators for matrix algebras converging to coadjoint orbits

In the high-energy physics literature one finds statements such as ``matrix algebras converge to the sphere''. Earlier I provided a general precise setting for understanding such statements, in which

Commutative geometry for non-commutative D-branes by tachyon condensation

There is a difficulty in defining the positions of the D-branes when the scalar fields on them are non-abelian. We show that we can use tachyon condensation to determine the position or the shape of

Poisson Lie groups, dressing transformations, and Bruhat decompositions

A Poisson Lie group is a Lie group together with a compatible Poisson structure. The notion of Poisson Lie group was first introduced by Drinfel'd [2] and studied by Semenov-Tian-Shansky [17] to
...