2013/09/01 by V. N. Rodionov, Rodionov, V. N. · 1 citation
Mathematics · Physics and Astronomy · #Neutrino Physics Research #Quantum Mechanics and Non-Hermitian Physics #hep-ph #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1309.0231
17 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1303.7053
arxiv created 2013/09/01 · arxiv updated 2013/09/03
The modified Dirac equations for the massive particles with the replacement of the physical mass m with the help of the relation m→ m1 + γ5 m2 are investigated. It is shown that for a free fermion theory with a γ5 mass term, the finiteness of the mass spectrum at the value mmax= m12/2m2 takes place. In this case the region of the unbroken \cal PT-symmetry may be expressed by means of the simple restriction of the physical mass m≤ mmax. Furthermore, we have that the areas of unbroken \cal PT-symmetry m1≥ m2≥ 0, which guarantees the reality values of the physical mass m, consists of three different parametric subregions: i) 0≤ m2 < m1/√(2), ii) m2=m1/√(2)=mmax, (iii)m1/√(2)< m2 ≤ m1. It is vary important, that only the first subregion (i) defined mass values m1,m2, which correspond to the description of traditional particles in the modified models, because this area contain the possibility transform the modified model to the ordinary Dirac theory. The second condition (ii) is defined the "maximon" - the particle with maximal mass m=mmax. In the case (iii) we have to do with the unusual or "exotic" particles for description of which Hamiltonians and equations of motion have no a Hermitian limit. The formulated criterions may be used as a major test in the process of the division of considered models into ordinary and "exotic fermion theories".