Poisson Sigma Model and Semiclassical Quantization of Integrable Systems

In this paper, we outline the construction of semiclassical eigenfunctions of integrable models in terms of the semiclassical path integral for the Poisson sigma model with the target space being the phase space of the integrable system. The semiclassical path integral is defined as a formal power series with coefficients being Feynman diagrams. We also argue that in a similar way one can obtain irreducible semiclassical representations of Kontsevich’s star product.