The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems

TL;DR

This paper derives a symmetry constraint for super Dirac systems, transforming the hierarchy into finite-dimensional integrable Hamiltonian systems with explicit integrals of motion, advancing the understanding of supersymmetric integrability.

Contribution

It introduces an explicit Bargmann symmetry constraint and binary nonlinearization for super Dirac systems, providing a new approach to their integrability analysis.

Findings

Decomposition of super Dirac hierarchy into finite-dimensional systems

Explicit integrals of motion for Liouville integrability

Establishment of supersymmetric Hamiltonian systems

Abstract

An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the supersymmetry manifold $R^{4N|2N}$ with the corresponding dynamical variables $x$ and $t_n$. The integrals of motion required for Liouville integrability are explicitly given.