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International Journal of Theoretical Physics

, Volume 54, Issue 3, pp 933–950 | Cite as

Extended Supersymmetric Quantum Mechanics Algebras in Scattering States of Fermions off Domain Walls

  • Konstantinos Kleidis
  • Vasilis K. Oikonomou
Article

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.

Keywords

Supersymmetric quantum mechanics Domain walls Superconducting domail walls Localized fermions 

Notes

Acknowledgments

Financial support by the Research Committee of the Technological Education Institute of Central Macedonia, under grant SAT/ME/100414-86/06, is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTechnological Education Institute of Central MacedoniaSerresGreece

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