The Quantum Hydrodynamics of the Sutherland Model

TL;DR

This paper explores the quantum hydrodynamics of the Sutherland model, revealing how different inner products affect the hermiticity of the chiral and non-chiral Hamiltonians, thus clarifying the model's mathematical structure.

Contribution

It identifies the role of multiple inner products in ensuring hermiticity in the quantum hydrodynamics of the Sutherland model, clarifying the origin of the chiral condition.

Findings

Two distinct inner products make the chiral Hamiltonian hermitian.

Only one inner product ensures the hermiticity of the full Hamiltonian.

The form of the chiral condition is explained by these inner product differences.

Abstract

We show that the form of the chiral condition found by Abanov et al., in the quantum hydrodyamics of the Sutherland model arises because there are two distinct inner products with respect to which the chiral Hamitonian hermitian, but only one with respect to which the full, non-chiral, Hamiltonian is hermitian.