Geodesic
Developing a~non-Hermitian algebraic theory with the~$\gamma_5$-extension of mass
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 124-139

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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.
Mots-clés : maximum mass
Keywords: ferminonic sector, $PT$ symmetry, pseudo-Hermitian theory. 
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     author = {V. N. Rodionov and G. A. Kravtsova},
     title = {Developing {a~non-Hermitian} algebraic theory with the~$\gamma_5$-extension of mass},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a7/}
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V. N. Rodionov; G. A. Kravtsova. Developing a~non-Hermitian algebraic theory with the~$\gamma_5$-extension of mass. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 1, pp. 124-139. http://geodesic.mathdoc.fr/item/TMF_2015_182_1_a7/