The current algebra representations of quantum many-particle Schr\"odinger type Hamiltonian models, their factorized structure and integrability

TL;DR

This paper develops a current algebra approach to represent and analyze quantum many-particle Hamiltonians, revealing their factorized structure and integrability, with applications to well-known quantum integrable models.

Contribution

It introduces a novel current algebra representation scheme for quantum Hamiltonians, enabling algebraic reconstruction and analysis of their factorized and integrable structures.

Findings

Detailed analysis of Hamiltonian factorization in integrable models

Application to Calogero-Sutherland and nonlinear Schrödinger systems

Demonstration of algebraic reconstruction of symmetry operators

Abstract

There is developed a current algebra representation scheme for reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space and its application to quantum Hamiltonian and symmetry operators in case of quantum integrable spatially many- and one-dimensional dynamical systems. As examples, we have studied in detail the factorized structure of Hamiltonian operators, describing such quantum integrable spatially many- and one-dimensional models as generalized oscillatory, Calogero-Sutherland, Coulomb type and nonlinear Schr\"{o}dinger dynamical systems of spinless bose-particles.