The PT Symmeter

V.N.Rodionov

Starting with the modified Dirac equations for free massive particles with the γ5-extension of the physical mass \(m\to m_1+\gamma_5m_2\), we consider equations of relativistic quantum mechanics in the presence of an external electromagnetic field. The new approach is developing on the basis of existing methods for study the unbroken PT symmetry of Non-Hermitian Hamiltonians. The paper shows that this modified model contains the definition of the mass parameter, which may use as the determination of the magnitude scaling of energy M. Obviously that the transition to the standard approach is valid when small in comparison with M energies and momenta. Formally, this limit is performed when \(M\to\infty\), which simultaneously should correspond to the transition to a Hermitian limit \(m2\to0\). Inequality \(m\leq M\) may be considered and as the restriction of the mass spectrum of fermions considered in the model. Within of this approach, the effects of possible observability mass parameters: \(m_1, m_2, M\) are investigated taking into account the interaction of the magnetic field with charged fermions together with the accounting of their anomalous magnetic moments.

http://arxiv.org/abs/1404.0503
High Energy Physics – Theory (hep-th); High Energy Physics – Phenomenology (hep-ph); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

V.N.Rodionov

The modified Dirac equations for the massive particles with the replacement of 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 with a \(\gamma_5\) 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 the physical 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 of the 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 the first subregion (i) defined mass values \(m_1,m_2,\) 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 \(m=m_{max}\). 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”.

http://arxiv.org/abs/1309.0231
High Energy Physics – Theory (hep-th); High Energy Physics – Phenomenology (hep-ph); Mathematical Physics (math-ph); Quantum Physics (quant-ph)