Poisson sigma model and semiclassical quantization of integrable systems

TL;DR

This paper develops a method to construct semiclassical eigenfunctions of integrable systems using the Poisson sigma model's path integral, linking it to deformation quantization via Kontsevich's star product.

Contribution

It introduces a novel approach connecting semiclassical quantization of integrable systems with the Poisson sigma model and deformation quantization techniques.

Findings

Semiclassical eigenfunctions expressed through Feynman diagram series.

Irreducible semiclassical representations of Kontsevich's star product derived.

Framework bridges path integral methods with deformation quantization.

Abstract

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.