Abstract
Self-adjoint second-order equations with spinor wave functions in an external electromagnetic field are obtained for fermions. The relationship is found between these equations and the Dirac equations in the Foldy–Wouthuysen representation. Closed chiral symmetric equations are written for left and right spinors by using the Dirac matrices in chiral representation. A closed chiral symmetric Foldy–Wouthuysen equation is obtained for an arbitrary electromagnetic field. There are no summands mixing left and right spinors in these equations irrespective of the presence or absence of fermion mass.
Similar content being viewed by others
REFERENCES
P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed., Oxford: Clarendon Press, 1958.
Ya. B. Zel’dovich and V. S. Popov, Sov. Phys. Usp. 14, 673 (1972).
M. V. Gorbatenko, V. P. Neznamov, and E. Yu. Popov, J. Phys.: Conf. Ser. 678, 012037 (2016), (XVI Workshop on High Energy Spin Physics (D-SPIN2015)), doi 10.1088/1742-6596/678/1/012037; arXiv: 1511.05058 (gr-qc); VANT, Ser. Theor. Appl. Phys. 4, 21–31 (2015).10.1088/1742-6596/678/1/012037
L. L. Foldy and S. A. Wouthuysen, Phys. Rev. 78, 29 (1950).
K. M. Case, Phys. Rev. 95, 1323 (1954).
R. P. Feynman and M. Gell-Mann, Phys. Rev. 109, 193 (1958).
L. Brown, Phys. Rev. 111, 462 (1958).
V. P. Neznamov, Phys. Part. Nucl. 37, 86 (2006).
V. P. Neznamov, Phys. Part. Nucl. 43, 15 (2012).
L. D. Landau and E. M. Lifshitz, L. D. Landau and E. M. Lifshitz, Quantum Mechanics. Nonrelativistic Theory, Oxford: Pergamon Press, 1965.
V. P. Neznamov and I. I. Safronov, VANT, Ser. Theor. Appl. Phys. 4, 9–24 (2016).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by N. Semenova
Rights and permissions
About this article
Cite this article
Neznamov, V.P. Self-Adjoint Second-Order Equations for Fermions and the Foldy–Wouthuysen Representation. Phys. Part. Nuclei 49, 725–729 (2018). https://doi.org/10.1134/S1063779618040421
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063779618040421