2003/09/30 by S. Andrea, A. Restuccia, A. Sotomayor · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Applied mathematics #Biology #Economics #Genetics #Hierarchy #Kernel (algebra) #Korteweg–de Vries equation #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Sequence (biology) #hep-th
paper · pdf · doi:10.1063/1.1650047
published in Journal of Mathematical Physics 45(5), 1715-1729 (American Institute of Physics) · 20 pages, to be published in JMP
arxiv created 2004/01/28 · openalex publication_date 2004/04/16 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We introduce the free N=1 supersymmetric derivation ring and prove the existence of an exact sequence of supersymmetric rings and linear transformations. We apply necessary and sufficient conditions arising from this exact supersymmetric sequence to obtain the essential relations between conserved quantities, gradients and the N=1 super Korteweg–de Vries (KdV) hierarchy. We combine this algebraic approach with an analytic analysis of the super heat operator. We obtain the explicit expression for the Green’s function of the super heat operator in terms of a series expansion and discuss its properties. The expansion is convergent under the assumption of bounded bosonic and fermionic potentials. We show that the asymptotic expansion when t→0+ of the Green’s function for the superheat operator evaluated over its diagonal generates all the members of the N=1 super KdV hierarchy.