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

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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 182, Number 1, Pages 124–139
DOI: https://doi.org/10.4213/tmf8744 (Mi tmf8744)

This article is cited in 9 scientific papers (total in 9 papers)

Developing a non-Hermitian algebraic theory with the

γ_{5}

$\gamma_5$ -extension of mass

V. N. Rodionov^a, G. A. Kravtsova^b

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

Full-text PDF (487 kB) Citations (9)

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

Abstract: We consider a non-Hermitian fermionic model with the

γ_{5}

$\gamma_5$ -extension of mass:

m \to m_{1} + γ_{5} m_{2}

$m\to m_1+\gamma_5m_2$ . 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

P T

$PT$ -symmetry preservation in the theory. It implies segregating the initial domain of

P T

$PT$ -symmetry preservation into subdomains corresponding to descriptions of standard and exotic particles. We calculate the operator

C

$\mathcal C$ 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,

P T

$PT$ symmetry, pseudo-Hermitian theory.

Received: 23.06.2014

English version:
Theoretical and Mathematical Physics, 2015, Volume 182, Issue 1, Pages 100–113
DOI: https://doi.org/10.1007/s11232-015-0249-3

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. N. Rodionov, G. A. Kravtsova, “Developing a non-Hermitian algebraic theory with the

γ_{5}

$\gamma_5$ -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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Linking options:

https://www.mathnet.ru/eng/tmf8744

https://doi.org/10.4213/tmf8744

https://www.mathnet.ru/eng/tmf/v182/i1/p124

This publication is cited in the following 9 articles:

G. A. Kravtsova, V. N. Rodionov, “Quantum Electrodynamics with $\boldsymbol{\gamma}_{\mathbf{5}}$ Modified Dirac Field”, Moscow Univ. Phys., 77:2 (2022), 456
G. A. Kravtsova, “Algebraic quantum theory with maximal frequency”, Theoret. and Math. Phys., 208:2 (2021), 1051–1060
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
V. N. Rodionov, “Exotic fermions in Kadyshevsky's theory and the possibility to detect them”, Phys. Part. Nuclei, 48:2 (2017), 319–331
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
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
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
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
V. N. Rodionov, “Exact solutions For non-Hermitian Dirac-Pauli equation in an intensive magnetic field”, Phys. Scr., 90:4 (2015), 045302

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	64
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