Annotation
A non-Hermitian fermion model containing a $\gamma_5$-matrix in the mass term $m \rightarrow m_1 + \gamma_5 m_2$ is considered. A new refined condition of the unbroken $\cal PT$ - symmetry of the theory is proposed that comprises an indication that the initial domain of unbroken $\cal PT$ - symmetry is divided into subdomains corresponding to the description of ordinary and exotic particles. A relationship is established between the theory under study and the quantum field theory with maximal mass $M$ developed on the basis of the geometric approach. The operator {ie223-1} is calculated explicitly, which is required for the construction of a new scalar product in the theory with a non-Hermitian Hamiltonian.
Received: 2013 November 26
Approved: 2014 September 11
PACS:
02.30.Jr Partial differential equations
03.65.-w Quantum mechanics
03.65.Ge Solutions of wave equations: bound states
12.10.-g Unified field theories and models
03.65.-w Quantum mechanics
03.65.Ge Solutions of wave equations: bound states
12.10.-g Unified field theories and models
© 2016 Publisher M.V.Lomonosov Moscow State University
Authors
V.N. Rodionov$^1$, G.A. Kravtsova$^2$
$^1$Department of Mathematical Economics and Informatics, Plekhanov Russian University of Economics, Moscow, 117997, Russia
$^2$Department of Physics, Moscow State University, Moscow, 119991, Russia
$^1$Department of Mathematical Economics and Informatics, Plekhanov Russian University of Economics, Moscow, 117997, Russia
$^2$Department of Physics, Moscow State University, Moscow, 119991, Russia