Advertisement

Russian Physics Journal

, Volume 61, Issue 8, pp 1376–1382 | Cite as

Violation of the Equivalence Principle in Non-Hermitian Fermion Theory

  • V. N. Rodionov
  • A. M. Mandel
ELEMENTARY PARTICLE PHYSICS AND FIELD THEORY

Consequences of the non-Hermitian expansion of the Dirac equation in which the mass term is written in the form m → m1 + γ5m2 are considered. It is shown that such procedure inevitably leads to violation of the weak equivalence principle, i.e., causes an inequality of gravitational and inert fermion masses. However, if to relate the Hermitian, m1, and non-Hermitian, m2, masses by the additional condition m2/m1 = m1/2M ≤ 1, the possibility arises to preserve the equivalence principle for fermions of the standard model with high accuracy. In this case, the parameter M = const is the universal constant with dimensionality of mass that can be related to a maximum possible allowed fermion mass in this model. As a consequence of the same condition, a new class of solutions of the modified Dirac equation arises that describes particles whose properties make them obvious candidates for dark matter.

Keywords

modified Dirac equation non-Hermitian expansion violation of the equivalence principle dark matter 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. G. Kadyshevsky, Nucl. Phys. B, 141, 477 (1978); Fermilab-Pub. 78/22-THY (1978); Fermilab-Pub. 78/70-THY (1978).Google Scholar
  2. 2.
    C. M. Bender and S. Boettcher, Phys. Rev. Lett., 80, 5243 (1998).ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Non-Hermitian Hamiltonians in Quantum Physics: Selected Contributions from the 15th Int. Conf. on Non-Hermitian Hamiltonians in Quantum Physics, Palermo, Italy, Springer Proceedings in Physics, Vol. 184 (2015).Google Scholar
  4. 4.
    V. N. Rodionov and G. A. Kravtsov, Vestn. Mosk. Univ., Ser. 3. Fiz. Astron. No. 3, 20 (2014).Google Scholar
  5. 5.
    V. G. Krechet, Sov. Phys. J., 29, No. 10, 790 (1986).CrossRefGoogle Scholar
  6. 6.
    C. M. Bender, H. F. Jones, and R. J. Rivers, Phys. Lett. B, 625, 333 (2005).ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Particle Data Group, The universality of the coupling between matter and gravity (Equivalence Principle) has been verified around the level 10–13 (2017).Google Scholar
  8. 8.
    V. B. Berestetskii, E. M. Lifshits, and A. P. Pitaevskii, Theoretical Physics. Vol. 4. Quantum Electrodynamics [in Russian], Nauka, Moscow (1980).Google Scholar
  9. 9.
    J. Alexandre, C. M. Bender, and P. Millington, arXiv:1703.05251v1 (2017).Google Scholar
  10. 10.
    V. N. Rodionov and A. M. Mandel, arXiv:1708.08394v1 (2017).Google Scholar
  11. 11.
    A. I. Ansel’m, Introduction to the Theory of Semiconductors [in Russian], Nauka, Moscow (1978).Google Scholar
  12. 12.
    V. N. Rodionov and G. A. Kravtsova, Phys. Part. Nucl., 47, 252 (2016).CrossRefGoogle Scholar
  13. 13.
    Ya. B. Zeldovich and I. D. Novikov, Structure and Evolution of the Universe [in Russian], Nauka, Moscow (1975).Google Scholar
  14. 14.
    M. G. Makris and P. Lambropoulos, Phys. Rev. A, 70, 044101 (2004).ADSCrossRefGoogle Scholar
  15. 15.
    S. Esterhazy et al., Phys. Rev. A, 90, 023816 (2014).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Plekhanov Russian University of EconomicsMoscowRussia
  2. 2.Moscow State Technological University “STANKIN,”MoscowRussia

Personalised recommendations