Quantum-Mechanical Description of the Fermionic Doublet and its Link with the Dirac Equation
Keywords:fermionic doublet, Dirac equation, Schr¨odinger–Foldy equation
A brief review of the diﬀerent ways of the Dirac equation derivation is given. The foundations of the relativistic canonical quantum mechanics of a fermionic doublet on the basis of the Schr¨odinger–Foldy equation of motion are formulated. In our approach, the Dirac equation is derived from the Schr¨ odinger–Foldy equation.
L. Foldy and S. Wouthuysen, Phys. Rev. 78, 29 (1950).
L. Foldy, Phys. Rev. 102, 568 (1956).
L. Foldy, Phys. Rev. 122, 275 (1961).
E. Salpeter, Phys. Rev. 87, 328 (1952).
W. Lucha and F. Schobert, Phys. Rev. A. 54, 3790 (1996).
Y. Chargui and A. Trabelsi, Phys. Lett. A 377, 158 (2013).
I. Krivsky, V. Simulik, I. Lamer, and T. Zajac, arXiv: 1301.6343 [math-ph] 27 Jan 2013.
I. Krivsky, V. Simulik, I. Lamer, and T. Zajac, TWMS J. App. Eng. Math. 3, 62 (2013).
I. Krivsky, V. Simulik, T. Zajac, and I. Lamer, in: Proceedings of the 14-th Int. Conference "Mathematical Methods in Electromagnetic Theory", August 28–30, 2012 (Institute of Radiophysics and Electronics, Kharkiv, 2012), pp. 201– 204.
N. Bogoliubov, A. Logunov, and I. Todorov, Foundations of the Axiomatic Approach in Quantum Field Theory (Nauka, Moscow, 1969) (in Russian).
V. Simulik and I. Krivsky, Dopov. NAN Ukr., No. 5, 82 (2010).
I. Krivsky and V. Simulik, Cond. Matt. Phys. 13, 43101 (2010).
V. Simulik and I. Krivsky, Phys. Lett. A 375, 2479 (2011).
V. Simulik, I. Krivsky, and I. Lamer, TWMS J. App. Eng. Math. 3, 46 (2013).
V. Simulik and I. Krivsky, Ukr. J. Phys. 58, 523 (2013).
P. Dirac, The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1958).
N. Bogoliubov and D. Shirkov, Introduction to the Theory of Quantized Fields (Wiley, New York, 1980).
J. Sakurai, Advanced Quantum Mechanics (Addison– Wesley, New York, 1967).
L. Ryder, Quantum Field Theory (Cambridge Univ. Press, Cambridge, 1996).
J. Keller, Theory of the Electron. A Theory of Matter from START (Kluwer, Dordrecht, 2001).
V. Fock and D. Iwanenko, Z. Phys. 54, 798 (1929).
V. Fock, Z. Phys. 57, 261 (1929).
A. Wightman, in Dispersion Relations and Elementary Particles, edited by C. De Witt and R. Omnes (Wiley, New York, 1960), p. 291.
H. Sallhofer, Z. Naturforsch. A 33, 1378 (1978).
H. Sallhofer, Z. Naturforsch. A 41, 468 (1986).
S. Strinivasan and E. Sudarshan, J. Phys. A 29, 5181 (1996).
L. Lerner, Eur. J. Phys. 17, 172 (1996).
T. Kubo, I. Ohba, and H. Nitta, Phys. Lett. A 286, 227 (2001).
H. Cui, arXiv: quant-ph/0102114, Aug. 15, 2001.
Y.J. Ng and H. van Dam, arXiv: hep-th/0211002, Feb. 4, 2003.
M. Calerier and L. Nottale, Electromagn. Phen. 3(9), 70 (2003).
M. Evans, Found. Phys. Lett. 16, 369 (2003).
M. Evans, Found. Phys. Lett. 17, 149 (2004).
V.M. Simulik and I.Yu. Krivsky, Rep. Math. Phys. 50, 315 (2002).
V.M. Simulik and I.Yu. Krivsky, Electromagn. Phen. 3(9), 103 (2003).
V.M. Simulik, in What is the Electron?, edited by V.M. Simulik (Apeiron, Montreal, 2005), p. 109.
V. Vladimirov, Methods of the Theory of Generalized Functions (Taylor and Francis, London, 2002).
von J. Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932).
G. Bluman and S. Anco, Symmetry and Integration Methods for Differential Equations (Springer, New York, 2002).
J.P. Elliott and P.J. Dawber, Symmetry in Physics (Macmillan Press, London, 1979), Vol. 1.
B.G. Wybourne, Classical Groups for Physicists (Wiley, New York, 1974).
H. Bondi, Rev. Mod. Phys. 29, 423 (1957).
E. Recami, and G. Zino, Nuovo Cim. A 33, 205 (1976).
G. Landis, Journ. Propulsion and Power 7, 304 (1991).
R. Wayne, Turk. J. Phys. 36, 165 (2012).
W. Kuellin, P. Gaal, K. Reimann, T. Worner, T. Elsaesser, and R. Hey, Phys. Rev. Lett. 104, 146602(1-4) (2010).
V.P. Neznamov, Phys. Part. Nucl. 37, 86 (2006).
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.