Theoretical and Mathematical Physics

, Volume 198, Issue 3, pp 412–424 | Cite as

Restriction of the Fermion Mass Spectrum in PT-Symmetric Systems and its Implications For Studying Dark Matter

  • V. N. RodionovEmail author
  • A. M. Mandel
  • G. A. Kravtsova


We formulate principal positions of a non-Hermitian model with a γ5-extension of the fermion mass, which are often neglected in investigating this subject. A consistent approach to this problem requires the constraint m ≤ M, where M bounds the entire fermion mass spectrum. An analogous approach was proposed in the geometric model, which can be regarded as the first PT-symmetric non-Hermitian fermion model with a γ5-extension of mass. Exotic particles appear in both these theories. A detailed consideration of the properties of these particles allows conjecturing that they are possible candidates in the structure of dark matter. We also discuss a simple estimate for determining the maximum admissible value of the fermion mass M.


mass spectrum restriction two zones of PT symmetry two-mass paradox exotic particle 


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • V. N. Rodionov
    • 1
    Email author
  • A. M. Mandel
    • 2
  • G. A. Kravtsova
    • 3
  1. 1.Plekhanov Russian University of EconomicsMoscowRussia
  2. 2.State University STANKINMoscowRussia
  3. 3.Lomonosov Moscow State UniversityMoscowRussia

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