Supersymmetry and exceptional points

Miloslav Znojil

doi:10.3390/sym892060012

Supersymmetry and exceptional points

High Energy Physics - Theory 2025-11-27 v1 Mathematical Physics math.MP Quantum Physics

Authors: Miloslav Znojil

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Abstract

A conceptual bridge is provided between SUSY and the three-Hilbert-space upgrade of quantum theory a.k.a. ${\cal PT}-$ symmetric or quasi-Hermitian. In particular, a natural theoretical link is found between SUSY and the presence of Kato's exceptional points (EPs), both being related to the phenomenon of degeneracy of energy levels. Regularized spiked harmonic oscillator is recalled for illustration.

Keywords

exceptional points non-hermitian quantum mechanics pt-symmetry

Cite

@article{arxiv.2005.04508,
  title  = {Supersymmetry and exceptional points},
  author = {Miloslav Znojil},
  journal= {arXiv preprint arXiv:2005.04508},
  year   = {2025}
}

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22 pages, 3 pictures

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