Quantum dispersionless KdV hierarchy revisited

TL;DR

This paper develops a quantum version of the dispersionless KdV hierarchy using vertex algebra techniques, providing new insights into its quantization and eigenvalue structure.

Contribution

It introduces a novel non-associative Weyl quantization method for the quantum dispersionless KdV hierarchy and analyzes its eigenvalue problem.

Findings

Constructed the quantum dispersionless KdV hierarchy

Applied Heisenberg vertex algebra to quantize Hamiltonian structures

Computed eigenvalues for the quantum hierarchy

Abstract

We quantize Hamiltonian structures with hydrodynamic leading terms using the Heisenberg vertex algebra. As an application, we construct the quantum dispersionless KdV hierarchy via a non-associative Weyl quantization procedure and compute the corresponding eigenvalue problem.