• Corpus ID: 245837208

Strict quantization of polynomial Poisson structures

@inproceedings{Barmeier2022StrictQO,
  title={Strict quantization of polynomial Poisson structures},
  author={Severin Barmeier and Philipp Schmitt},
  year={2022}
}
We show how combinatorial star products can be used to obtain strict deformation quantizations of polynomial Poisson structures on R, generalizing known results for constant and linear Poisson structures to polynomial Poisson structures of arbitrary degree. We give several examples of nonlinear Poisson structures and construct explicit formal star products whose deformation parameter can be evaluated to any real value of ~, giving strict quantizations on the space of analytic functions on R… 

References

SHOWING 1-10 OF 27 REFERENCES

Fréchet algebraic deformation quantization of the Poincaré disk

Starting from formal deformation quantization we use an explicit formula for a star product on the Poincaré disk Dn to introduce a Fréchet topology making the star product continuous. To this end a

Deformation Quantization of Poisson Manifolds

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the

Deformation quantization of algebraic varieties

The paper is devoted to peculiarities of the deformation quantization in the algebro-geometric context. A direct application of the formality theorem to an algebraic Poisson manifold gives a

On Quantization of Quadratic Poisson Structures

Abstract: 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

Convergent star products for projective limits of Hilbert spaces

A Nuclear Weyl Algebra

Multiple zeta values in deformation quantization

Kontsevich's 1997 formula for the deformation quantization of Poisson brackets is a Feynman expansion involving volume integrals over moduli spaces of marked disks. We develop a systematic theory of

Convergence of the Gutt Star Product

In this work we consider the Gutt star product viewed as an associative deformation of the symmetric algebra S^\bullet(g) over a Lie algebra g and discuss its continuity properties: we establish a

Deformation quantizations with separation of variables on a Kähler manifold

We give a simple geometric description of all formal differentiable deformation quantizations on a Kähler manifoldM such that for each open subsetU⊂M ⋆-multiplication from the left by a holomorphic