The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of Super KdV equations

TL;DR

This paper derives the Hamiltonian structure of a coupled KdV system resulting from supersymmetric breaking of Super KdV equations, demonstrating its physical viability through boundedness from below.

Contribution

It introduces a novel Hamiltonian formulation for a supersymmetry-broken coupled KdV system using Dirac's method and Clifford algebra.

Findings

Hamiltonian is bounded from below.

The system is physically admissible.

New Hamiltonian structure derived from supersymmetry breaking.

Abstract

A supersymmetric breaking procedure for $N=1$ Super KdV, using a Clifford algebra, is implemented. Dirac's method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting solitonic system of coupled Korteweg-de Vries type system. It is shown that the Hamiltonian obtained by this procedure is bounded from below and in that sense represents a model which is physically admissible.