# Extended Supersymmetric Quantum Mechanics Algebras in Scattering States of Fermions off Domain Walls Source: [Extended Supersymmetric Quantum Mechanics Algebras in Scattering States of Fermions off Domain Walls]() Collection index: [llms.txt]() Data updated: 2025-10-24T16:21:17.711Z Authors: V.K. oikonomou, K. Kleidis Published: 2014-08-07T11:56:23.000Z ## Abstract We study the underlying extended supersymmetric structure in a system composed of fermions scattered off an infinitely extended static domain wall in the $xz$-plane. As we shall demonstrate, the fermionic scattered states are associated to two $N=2$ one dimensional supersymmetric quantum mechanical algebras with zero central charge. These two symmetries are combined to form a non-trivial one dimensional $N=4$ superalgebra with various central charges. In addition, we form higher dimensional irreducible representations of the two $N=2$ algebras. Moreover, we study how the Witten index behaves under compact odd and even perturbations, coming from a background magnetic field and some non-renormalizable Yukawa mass terms for the fermions. As we shall demonstrate, the Witten index is invariant only when the magnetic field is taken into account and particularly when only the $z$-component of the field is taken into account. Finally, we study the impact of this supersymmetric structures on the Hilbert space of the fermionic states and also we present a deformed extension of the $N=2$ supersymmetric structure. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()