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Pseudo-Hermitian Systems, Involutive Symmetries and Pseudofermions

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Abstract

We have briefly analyzed the existence of the pseudofermionic structure of multilevel pseudo-Hermitian systems with odd time-reversal and higher order involutive symmetries. We have shown that 2N-level Hamiltonians with N- order eigenvalue degeneracy can be represented in the oscillator-like form in terms of pseudofermionic creation and annihilation operators for both real and complex eigenvalues. The example of most general four-level traceless Hamiltonian with odd time-reversal symmetry, which is an extension of the SO(5) Hermitian Hamiltonian, is considered in greater and explicit detail.

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Authors and Affiliations

  1. Faculty of Physics, Theoretical Physics Laboratory, University of Science and Technology Houari Boumediene, BP 32, El Alia, Algiers, 16111, Algeria

    O. Cherbal & M. Zenad

  2. Institute for Nuclear Research and Nuclear Energy, 72 Tzarigradsko chaussee, 1784, Sofia, Bulgaria

    D. Trifonov

Authors
  1. O. Cherbal
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  2. D. Trifonov
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  3. M. Zenad
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Cherbal, O., Trifonov, D. & Zenad, M. Pseudo-Hermitian Systems, Involutive Symmetries and Pseudofermions. Int J Theor Phys 55, 5318–5330 (2016). https://doi.org/10.1007/s10773-016-3151-3

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  • DOI: https://doi.org/10.1007/s10773-016-3151-3

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