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Developing a non-Hermitian algebraic theory with the γ 5-extension of mass

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Abstract

We consider a non-Hermitian fermionic model with the γ5-extension of mass: m → m1 + γ5m2. 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 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.

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Authors and Affiliations

  1. Plekhanov Russian University of Economics, Moscow, Russia

    V. N. Rodionov

  2. Lomonosov Moscow State University, Moscow, Russia

    G. A. Kravtsova

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  1. V. N. Rodionov
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  2. G. A. Kravtsova
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Correspondence to V. N. Rodionov.

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__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 182, No. 1, pp. 124–139, January, 2014.

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Rodionov, V.N., Kravtsova, G.A. Developing a non-Hermitian algebraic theory with the γ 5-extension of mass. Theor Math Phys 182, 100–113 (2015). https://doi.org/10.1007/s11232-015-0249-3

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