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

  • V. N. RodionovEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 184)

Abstract

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 and Boettcher Phys Rev Lett 80:5243, 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 (\(\mathcal{PT}\)) 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 \(\mathcal{PT}\)-symmetric optics, where for several years produced not only theoretical but experimental studies.

Keywords

Maximal Mass Anomalous Magnetic Moment Bohr Magneton Mass Extension Neutrino Magnetic Moment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    C.M. Bender, S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    C.M. Bender, H.F. Jones, R.J. Rivers, Phys. Lett. B 625, 333 (2005)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    V.N. Rodionov, Exact Solutions for Non-Hermitian Dirac-Pauli Equation in an intensive magnetic field, (2014). arXiv:1406.0383
  4. 4.
    V.N. Rodionov, G.A. Kravtsova, Moscow Univ. Phys. Bull. N 3, 20 (2014)MathSciNetGoogle Scholar
  5. 5.
    V.N. Rodionov, G.A. Kravtsova, Teoretical Math. Phys. 182(1), 100 (2015)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    M. Znojil, Phys. Rev. D 80, 045022 (2009)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    A. Mostafazadeh, J. Math. Phys. 43 (2002), 205; 43, 2814 (2002)Google Scholar
  8. 8.
    C.M. Bender, D.C.Brody, J. Chen, H.F. Jones, K.A. Milton, M.C. Ogilvie, Phy. Rev. D 74 025016 (2006)Google Scholar
  9. 9.
    V.G. Kadyshevsky, Nucl. Phys. B141, 477 (1978); in Proceedings of International Integrative Conference on Group theory and Mathematical Physics (Austin, Texas, 1978); Fermilab-Pub. 78/70-THY, Sept. (1978); Phys. Elem. Chast. Atom. Yadra, 11, 5 (1980)Google Scholar
  10. 10.
    V.G. Kadyshevsky, M.D. Mateev, V.N. Rodionov, A.S. Sorin, Dokl. Phys. 51, 287 (2006), e-Print:hep-ph/0512332Google Scholar
  11. 11.
    V.G. Kadyshevsky, M.D. Mateev, V.N. Rodionov, A.S. Sorin, Towards a maximal mass model. CERN TH/2007-150; hep-ph/0708.4205Google Scholar
  12. 12.
    V.N. Rodionov, Phys. Scr. 90, 045302 (2015)ADSCrossRefGoogle Scholar
  13. 13.
    V.N. Rodionov, Int. J. Theor Phys. 54(11), 3907–3919 (2015). doi: 10.1007/s10773-014-2410-4
  14. 14.
    M.A. Markov, Prog. Theor. Phys. Suppl., Commemoration issue for the thirtieth anniversary of meson theory and Dr. H. Yukawa, p. 85 (1965). Sov. Phys. JETP 24, 584 (1967)Google Scholar
  15. 15.
    P.A.M. Dirac, The relativistic electron wave equation/preprint KFKI-1977-62 (Hungarian Academy of Sciences, Budapest); Central Res. Inst. Phy. 19, 1977 (1977)Google Scholar
  16. 16.
    J. Schwinger, Proc. Nat. Acad. Sci. USA 37, 152 (1951)Google Scholar
  17. 17.
    I.M. Ternov, V.R. Khalilov, V.N. Rodionov, Interaction of Charged Particles with Intensive Electromagnetic Field (Moscow State University Press, Moscow, 1982)Google Scholar
  18. 18.
    V.N. Rodionov, Phys. Rev. A 75, 062111 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    V.G. Kadyshevsky, V.N. Rodionov. Phys. Part. Nucl. 36(1), S34 (2005)Google Scholar
  20. 20.
    V.N. Rodionov, JETP 98, 395 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    I.M. Ternov, V.G. Bagrov, VCh. Zhukovskii, Moscow Univ. Phys. Bull. 1, 30 (1966)Google Scholar
  22. 22.
    B. Lee, R. Shrock, Phys. Rev. D. 16, 1444 (1977)ADSCrossRefGoogle Scholar
  23. 23.
    K. Fujikawa, R. Shrock, Phys. Rev. Let. 45, 963 (1980)ADSCrossRefGoogle Scholar
  24. 24.
    A. Beda, V. Brudanin et al., Adv. High Energy Phys. 350150 (2012)Google Scholar
  25. 25.
    C. Giunti, K.A. Kouzakov et al., Electromagnetic neutrinos in terrestrial experiments and astrophysics, (2015), (2005). arXiv:1506.05387

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Plekhanov Russian University of EconomicsMoscowRussia

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