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

Kravtsova

2016

EPJ Web Conf.

Abstract. Non-Hermitian fermion Hamiltonian with γ 5 mass extension is studied. The connection of this PT -symmetrical pseudo-Hermitian model with the geometrical theory with maximal mass is established. The interaction of modified Dirac particles with the external magnetic field is considered. In particular, modified neutrinos is under studying. The results of neutrinos mass values measurements are explained.

Section: Algebraic Theory With Maximal Massmentioning

confidence: 98%

“…(see [38], [39], [40]). It is so-called non-disturbed PT-symmetry in the theory when m is real, t.e.…”

Section: Algebraic Theory With Maximal Massmentioning

confidence: 99%

“…Very important feature of Algebraic Theory is that there exists a parameter of maximal mass in it. Indeed, due to simple mathematical manipulations one can find ( [39], [40]), that…”

Section: Algebraic Theory With Maximal Massmentioning

confidence: 99%

Section: Algebraic Theory With Maximal Massmentioning

confidence: 99%

Section: Algebraic Theory With Maximal Massmentioning

confidence: 99%

See 3 more Smart Citations

Non-Hermitian quantum theory with maximal mass

Kravtsova

2016

EPJ Web Conf.

Non-Hermitian $$\mathcal{PT}$$ PT -Symmetric Relativistic Quantum Theory in an Intensive Magnetic Field

Springer Proceedings in Physics

2016

Self Cite

We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of physical parameters. This condition not only guarantees the reality of the eigenvalues of Hamiltonian operators, but also implies the preservation of the probabilities of the considered quantum processes. However as it was shown relatively recently (Bender, Boettcher 1998), Hermiticity is a sufficient but it is not a necessary condition. It turned out that among non-Hermitian Hamiltonians it is possible to allocate a number of such which have real energy spectra and can ensure the development of systems over time with preserving unitarity. This type of Hamiltonians includes so-called parity-time (PT ) symmetric models which is already used in various fields of modern physics. The most developed in this respect are models, which used in the field of PT -symmetric optics, where for several years produced not only theoretical but experimental studies.

Non-Hermitian P T $\mathcal {P}\mathcal {T}$ -Symmetric Dirac-Pauli Hamiltonians with Real Energy Eigenvalues in the Magnetic Field

2014

Int J Theor Phys

Self Cite

The modified Dirac-Pauli equations, which is entered by means of γ 5 -mass extension of Hamiltonian operators, are considered. We also take into account the interaction of fermions with the intensive homogenous magnetic field focusing attention on (g-2) gyromagnetic factor of particles with spin 1/2. Without the use of perturbation theory in the external field the exact energy spectra are deduced with regard to spin effects of fermions. We discuss the possible proposals of experimental measuring of properties of new particles which arising in this model.