English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The modified Dirac equations for the massive particles with the replacementof the physical mass $m$ with the help of the relation $m\rightarrow m_1 +\gamma_5 m_2$ are investigated. It is shown that for a free fermion theory witha $\gamma_5$ mass term, the finiteness of the mass spectrum at the value $m_{max}= {m_1}^2/2m_2$ takes place. In this case the region of the unbroken$\cal PT$-symmetry may be expressed by means of the simple restriction of thephysical mass $m\leq m_{max}$. Furthermore, we have that the areas of unbroken$\cal PT$-symmetry $m_1\geq m_2\geq 0$, which guarantees the reality values ofthe physical mass $m$, consists of three different parametric subregions: i)$0\leq m_2 < m_1/\sqrt{2}$, \,\,ii) $m_2=m_1/\sqrt{2}=m_{max},$\,\,(iii)$m_1/\sqrt{2}< m_2 \leq m_1$. It is vary important, that only thefirst subregion (i) defined mass values $m_1,m_2,$ which correspond to thedescription of traditional particles in the modified models, because this areacontain the possibility transform the modified model to the ordinary Diractheory. The second condition (ii) is defined the "maximon" - the particle withmaximal mass $m=m_{max}$. In the case (iii) we have to do with the unusual or"exotic" particles for description of which Hamiltonians and equations ofmotion have no a Hermitian limit. The formulated criterions may be used as amajor test in the process of the division of considered models into ordinaryand "exotic fermion theories".

On limitation of mass spectrum in non-Hermitian $\cal PT$-symmetric models with the $\gamma_5$-dependent mass term