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TMF, 2015, Volume 182, Number 1, Pages 124–139 (Mi tmf8744)  

This article is cited in 7 scientific papers (total in 7 papers)

Developing a non-Hermitian algebraic theory with the $\gamma_5$-extension of mass

V. N. Rodionova, G. A. Kravtsovab

a Plekhanov Russian University of Economics, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia

Abstract: We consider a non-Hermitian fermionic model with the $\gamma_5$-extension of mass: $m\to m_1+\gamma_5m_2$. We establish the relation between this theory and a geometric theory with the maximum mass in the quantum mechanical approximation. We propose a more detailed condition of $PT$-symmetry preservation in the theory. It implies segregating the initial domain of $PT$-symmetry preservation into subdomains corresponding to descriptions of standard and exotic particles. We calculate the operator $\mathcal C$ in the new scalar product in such a theory with a non-Hermitian Hamiltonian and describe some consequences of introducing this operator. We find the eigenvalues and eigenvectors of this Hamiltonian.

Keywords: maximum mass, ferminonic sector, $PT$ symmetry, pseudo-Hermitian theory

DOI: https://doi.org/10.4213/tmf8744

Full text: PDF file (487 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 182:1, 100–113

Bibliographic databases:

Received: 23.06.2014

Citation: V. N. Rodionov, G. A. Kravtsova, “Developing a non-Hermitian algebraic theory with the $\gamma_5$-extension of mass”, TMF, 182:1 (2015), 124–139; Theoret. and Math. Phys., 182:1 (2015), 100–113

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Rodionov, “Non-Hermitian $\mathcal{PT}$-symmetric Dirac-Pauli Hamiltonians with real energy eigenvalues in the magnetic field”, Int. J. Theor. Phys., 54:11 (2015), 3907–3919  crossref  mathscinet  zmath  isi  scopus
    2. V. N. Rodionov, “Exact solutions For non-Hermitian Dirac-Pauli equation in an intensive magnetic field”, Phys. Scr., 90:4 (2015), 045302  crossref  isi  scopus
    3. V. N. Rodionov, G. A. Kravtsova, “An algebraic $\mathcal{PT}$-symmetric quantum theory with a maximal mass”, Phys. Part. Nuclei, 47:2 (2016), 135–156  crossref  mathscinet  isi  elib  scopus
    4. R. N. Vasilij, K. A. Galina, “Non-Hermitian quantum theory with maximal mass”, 19th International Seminar on High Energy Physics (Quarks-2016), Epj Web of Conferences, 125, eds. V. Andrianov, V. Matveev, V. Rubakov, V. Kim, A. Andrianov, M. Fitkevich, E D P Sciences, 2016, UNSP 05012  crossref  isi  scopus
    5. V. N. Rodionov, “Non-Hermitian $\mathcal{PT}$-symmetric relativistic quantum theory in an intensive magnetic field”, Non-Hermitian Hamiltonians in Quantum Physics, Springer Proceedings in Physics, 184, eds. F. Bagarello, R. Passante, C. Trapani, Springer-Verlag, Berlin, 2016, 357–369  crossref  isi  scopus
    6. V. N. Rodionov, “Exotic fermions in Kadyshevsky's theory and the possibility to detect them”, Phys. Part. Nuclei, 48:2 (2017), 319–331  crossref  isi  scopus
    7. V. N. Rodionov, A. M. Mandel, G. A. Kravtsova, “Restriction of the fermion mass spectrum in $PT$-symmetric systems and its implications for studying dark matter”, Theoret. and Math. Phys., 198:3 (2019), 412–424  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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