Year 2013,
Volume 3,
Issue 1,
62 - 74,
01.06.2013
Ivan KRİVSKY
Volodimir SİMULİK
Irina LAMER
Zajac TARAS
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
Ivan KRİVSKY
Volodimir SİMULİK
Irina LAMER
Zajac TARAS
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.