Formal Symplectic Realizations

@article{Cabrera2016FormalSR,
  title={Formal Symplectic Realizations},
  author={A. Cabrera and B. Dherin},
  journal={International Mathematics Research Notices},
  year={2016},
  volume={2016},
  pages={1925-1950}
}
We study the relationship between several constructions of symplectic realizations of a given Poisson manifold. Our main result is a general formula for a formal symplectic realization in the case of an arbitrary Poisson structure on $\R^n$. This formula is expressed in terms of rooted trees and elementary differentials, building on the work of Butcher, and the coefficients are shown to be a generalization of Bernoulli numbers appearing in the linear Poisson case. We also show that this… Expand
Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization

References

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