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Year 2013, Volume 3, Issue 1, 62 - 74, 01.06.2013

Abstract

References

  • [1] Krivsky, I., Simulik, V., Zajac, T. and Lamer, I., Derivation of the Dirac and Maxwell equations from the first principles of relativistic canonical quantum mechanics, // Proceedings of the 14-th Internat. Conference ”Mathematical Methods in Electromagnetic Theory” - 28-30 August 2012, Institute of Radiophysics and Electronics, Kharkiv, Ukraine, 201-204.
  • [2] Foldy, L. and Wouthuysen, S., (1950), On the Dirac theory of spin 1/2 particles and its non- relativistic limit, Phys. Rev. 78, 29-36.
  • [3] Foldy, L., (1956), Synthesis of covariant particle equations, Phys. Rev., 102, 568-581.
  • [4] Foldy, L., (1961), Relativistic particle systems with interaction, Phys. Rev., 122, 275-288.
  • [5] Bogolyubov, N.N., Logunov, A.A. and Todorov, I.T., (1969), Foundations of the axiomatic approach in quantum field theory, Nauka, Moskow, (in Russian).
  • [6] Fushchich, W.I. and Nikitin, A.G., (1994), Symmetries of equations of quantum mechanics, Allerton Press Inc., New York.
  • [7] Garbaczewski, P., (1986), Boson - Fermion duality in four dimensions: comments on the paper of Luther and Schotte, Internat. Journ. Theor. Phys., 25, 1193-1208.
  • [8] Vladimirov, V.S., (2002), Methods of the theory of generalized functions, Taylor and Francis, London.
  • [9] Simulik, V.M. and Krivsky, I.Yu., (2011), Bosonic symmetries of the Dirac equation, Phys. Lett. A., 375, 2479-2483.
  • [10] Simulik, V.M., Krivsky, I.Yu. and Lamer, I.L., (2012), Generalized Clifford - Dirac algebra and Fermi - Bose duality of the Dirac equation, Proceedings of the 14-th Internat. Conference ”Mathematical Methods in Electromagnetic Theory” - 28-30 August 2012, Institute of Radiophysics and Electronics, Kharkiv, Ukraine, 197-200.
  • [11] Von Neumann, J., (1996), Mathematical foundations of quantum mechanics, Princeton Univ. Press.
  • [12] Elliott, J.P. and Dawber, P.J., (1979), Symmetry in Physics, Vol.1, Macmillian Press, London.
  • [13] Wybourne, B.G., (1974), Classical groups for Physicists, John Wiley and sons, New York.

THE DIRAC EQUATION AS THE CONSEQUENCE OF THE QUANTUM-MECHANICAL SPIN 1/2 DOUBLET MODEL

Year 2013, Volume 3, Issue 1, 62 - 74, 01.06.2013

Abstract

The detailed consideration of the relativistic canonical quantum-mechanical model of an arbitrary −→s -multiplet is given. The group-theoretical analysis of the algebra of experimentally observable physical quantities for the s = 1 2 doublet is presented. It is shown that both the Foldy-Wouthuysen equation for the fermionic spin s = 1 2 doublet and the Dirac equation in its local representation are the consequences of the relativistic canonical quantum mechanics of the corresponding doublet. The mathematically welldefined consideration on the level of modern axiomatic approaches to the field theory is provided.

References

  • [1] Krivsky, I., Simulik, V., Zajac, T. and Lamer, I., Derivation of the Dirac and Maxwell equations from the first principles of relativistic canonical quantum mechanics, // Proceedings of the 14-th Internat. Conference ”Mathematical Methods in Electromagnetic Theory” - 28-30 August 2012, Institute of Radiophysics and Electronics, Kharkiv, Ukraine, 201-204.
  • [2] Foldy, L. and Wouthuysen, S., (1950), On the Dirac theory of spin 1/2 particles and its non- relativistic limit, Phys. Rev. 78, 29-36.
  • [3] Foldy, L., (1956), Synthesis of covariant particle equations, Phys. Rev., 102, 568-581.
  • [4] Foldy, L., (1961), Relativistic particle systems with interaction, Phys. Rev., 122, 275-288.
  • [5] Bogolyubov, N.N., Logunov, A.A. and Todorov, I.T., (1969), Foundations of the axiomatic approach in quantum field theory, Nauka, Moskow, (in Russian).
  • [6] Fushchich, W.I. and Nikitin, A.G., (1994), Symmetries of equations of quantum mechanics, Allerton Press Inc., New York.
  • [7] Garbaczewski, P., (1986), Boson - Fermion duality in four dimensions: comments on the paper of Luther and Schotte, Internat. Journ. Theor. Phys., 25, 1193-1208.
  • [8] Vladimirov, V.S., (2002), Methods of the theory of generalized functions, Taylor and Francis, London.
  • [9] Simulik, V.M. and Krivsky, I.Yu., (2011), Bosonic symmetries of the Dirac equation, Phys. Lett. A., 375, 2479-2483.
  • [10] Simulik, V.M., Krivsky, I.Yu. and Lamer, I.L., (2012), Generalized Clifford - Dirac algebra and Fermi - Bose duality of the Dirac equation, Proceedings of the 14-th Internat. Conference ”Mathematical Methods in Electromagnetic Theory” - 28-30 August 2012, Institute of Radiophysics and Electronics, Kharkiv, Ukraine, 197-200.
  • [11] Von Neumann, J., (1996), Mathematical foundations of quantum mechanics, Princeton Univ. Press.
  • [12] Elliott, J.P. and Dawber, P.J., (1979), Symmetry in Physics, Vol.1, Macmillian Press, London.
  • [13] Wybourne, B.G., (1974), Classical groups for Physicists, John Wiley and sons, New York.

Details

Primary Language English
Journal Section Research Article
Authors

Ivan KRİVSKY This is me
Institute of Electron Physics, National Academy of Sciences of Ukraine, 21 Universitetska Str., 88000 Uzhgorod, Ukraine


Volodimir SİMULİK This is me
Institute of Electron Physics, National Academy of Sciences of Ukraine, 21 Universitetska Str., 88000 Uzhgorod, Ukraine


Irina LAMER This is me
Institute of Electron Physics, National Academy of Sciences of Ukraine, 21 Universitetska Str., 88000 Uzhgorod, Ukraine


Zajac TARAS This is me
Uzhgorod National University, Department of Electronic Systems, 13 Kapitulna Str., 88000 Uzhgorod, Ukraine

Publication Date June 1, 2013
Published in Issue Year 2013, Volume 3, Issue 1

Cite

Bibtex @ { twmsjaem761696, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2013}, volume = {3}, number = {1}, pages = {62 - 74}, title = {THE DIRAC EQUATION AS THE CONSEQUENCE OF THE QUANTUM-MECHANICAL SPIN 1/2 DOUBLET MODEL}, key = {cite}, author = {Krivsky, Ivan and Simulik, Volodimir and Lamer, Irina and Taras, Zajac} }