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

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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.

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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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Authors and Affiliations

  1. Department of Mechanical Engineering, Technological Education Institute of Central Macedonia, 62124, Serres, Greece

    Konstantinos Kleidis & Vasilis K. Oikonomou

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  1. Konstantinos Kleidis
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  2. Vasilis K. Oikonomou
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Correspondence to Vasilis K. Oikonomou.

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Kleidis, K., Oikonomou, V.K. Extended Supersymmetric Quantum Mechanics Algebras in Scattering States of Fermions off Domain Walls. Int J Theor Phys 54, 933–950 (2015). https://doi.org/10.1007/s10773-014-2289-0

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  • DOI: https://doi.org/10.1007/s10773-014-2289-0

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