Symplectic field theory of a disk, quantum integrable systems, and Schur polynomials

TL;DR

This paper explores the quantization of Hamiltonians from the Hopf hierarchy within Symplectic Field Theory, revealing Schur polynomials as eigenvectors and applying this to compute the SFT potential of a disk.

Contribution

It establishes a connection between quantized Hamiltonians in SFT and Schur polynomials, providing a method to compute the SFT potential of a disk.

Findings

Schur polynomials form a complete set of eigenvectors for the quantized operators

Quantization of Hopf hierarchy Hamiltonians in SFT is explicitly characterized

The SFT potential of a disk is computed using these eigenvectors

Abstract

We consider commuting operators obtained by quantization of Hamiltonians of the Hopf (aka dispersionless KdV) hierarchy. Such operators naturally arise in the setting of Symplectic Field Theory (SFT). A complete set of common eigenvectors of these operators is given by Schur polynomials. We use this result for computing the SFT potential of a disk.