# 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

- Mathematics
- 2020

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

- Mathematics
- 1997

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

- Mathematics
- 2008

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

- Mathematics
- 2002

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…

### Multiple zeta values in deformation quantization

- Mathematics
- 2020

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

- Mathematics
- 2015

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

- Mathematics
- 1996

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…