Kazakh Mathematical Journal. 2019; : 6-20
Бозоны и лептоны в бикватернионном представлении. Периодическая система атомов как простая гамма
Аннотация
Построены частные монохроматические решения бикватернионных волновых уравнений для свободных полей электро-гравимагнитных зарядов и токов, которые описывают элементарные частицы, как стоячие монохроматические электро-гравимагнитные волны. Исследованы два класса решений этого биволнового уравнения, порожденные скалярными потенциалами (пульсары) и векторными потенциалами (спиноры). Исследованы их асимптотические свойства, на основании которых они классифицируются на тяжелые и легкие элементарные частицы (бозоны и лептоны). Показано, что бозоны представляют собой сферические гармонические пульсары, массовая плотность которых определяется частотой их колебаний. Это позволяет строить периодические системы элементарных частиц на основе классической музыкальной шкалы. В частности, дано бикватернионное представление атома водорода. На его основе построена периодическая система элементарных атомов, построенная по принципу простой музыкальной гаммы.
Список литературы
1. Alexeyeva L.A. Newtos’s laws for a biquaternionic model of the electro-gravimagnetic fields, chares, currents, and their interactions, Journal of Physical Mathematics, 1:1 (2009), Article ID S090604. https://doi.org/10.4303/jpm/S090604.
2. Alexeyeva L.A. Biquaternionic model of electro-gravimagnetic field, charges and currents. law of inertia, Journal of modern physics, 7:5 (2016), 435-444. https://doi.org/10.4236/jmp.2016.75045.
3. Alexeyeva L.A. Hamilton form of Maxwell equations and its generalized solutions, Differential equations, 39:6 (2003), 769-776.
4. Alekseeva L.A. Biquaternionic form of laws of electro-gravimagnetic charges and currents interactions, Journal of modern physics, 7:11 (2016), 1351-1358. https://doi.org/10.4236/jmp.2016.711121.
5. Alexeyeva L.A. Biquaternions algebra and its applications by solving of some theoretical physics equations, Int. J. Clifford Analysis, Clifford Algebras and Their Applications, 7:1 (2012), 19-39.
6. Alexeyeva L.A. Differential algebra of biquaternions. 4. Twistors and twistor fields, Mathematical Journal, 13 (2013) 17-35 (in Russian).
7. Vladimirov V.S. Generalized functions in mathematical physics, Moscow, Nauka, 1978 (in Russian).
8. Handbook of mathematical functions with formulas, graphs and mathematical tables, Edited by M. Abramovitz, I.A. Stegun. National bureau of standard, Applied mathematics series-55, 1964.
9. Shilov G.E. Simple gamut, Moscow state university, 1970 (in Russian).
10. Alexeyeva L.A. Differential Algebra of Biquaternions. Dirac Equation and Its Generalized Solutions, Progress in Analysis. Proceedings of the 8-th Congress of the ISAAC, Moscow, 22-27 August, (2013), 153-161.
11. Lyudmila Alexeyeva Periodic system of atoms in biquaternionic representation, Journal of Modern Physics, 9:8 (2018), 1633-1644. https://doi.org/10.4236/jmp.2018.98102.
12. Alexeyeva L.A. Periodic system of atoms as simple gamma in biquaternionic representation, Scientific federation, Abstracts of 2nd International conference on Quantum Mechanics and Nuclear Engineering. Keynote forum. Paris, 23-24 September, (2019), P. 56.
Kazakh Mathematical Journal. 2019; : 6-20
Bosons and leptons in biquaternionic representation. Periodic system of atoms as simple gamma
Abstract
Particular monochromatic solutions of biquaternionic wave for the free fields of electro-gravimagnetic charges and currents have been constructed that describe elementary particles as standing monochromatic electro-gravimagnetic waves. Two classes solutions of this biwave equation generated by scalar potentials (pulsars) and vectorial potentials (spinors) are studied. Their asymptotic properties have been researched on the basis of which they are classified on heavy and light elementary particles (bosons and leptons). It is shown that bosons are spherical harmonic pulsars, the mass density of which is determined by their frequency of oscillations. This allows to construct periodic systems of elementary particles on the basis of classical musical scale. In particular, a biquaternionic representation of the hydrogen atom is given and advising it a periodic system, built on the principle of the simple musical scale.
References
1. Alexeyeva L.A. Newtos’s laws for a biquaternionic model of the electro-gravimagnetic fields, chares, currents, and their interactions, Journal of Physical Mathematics, 1:1 (2009), Article ID S090604. https://doi.org/10.4303/jpm/S090604.
2. Alexeyeva L.A. Biquaternionic model of electro-gravimagnetic field, charges and currents. law of inertia, Journal of modern physics, 7:5 (2016), 435-444. https://doi.org/10.4236/jmp.2016.75045.
3. Alexeyeva L.A. Hamilton form of Maxwell equations and its generalized solutions, Differential equations, 39:6 (2003), 769-776.
4. Alekseeva L.A. Biquaternionic form of laws of electro-gravimagnetic charges and currents interactions, Journal of modern physics, 7:11 (2016), 1351-1358. https://doi.org/10.4236/jmp.2016.711121.
5. Alexeyeva L.A. Biquaternions algebra and its applications by solving of some theoretical physics equations, Int. J. Clifford Analysis, Clifford Algebras and Their Applications, 7:1 (2012), 19-39.
6. Alexeyeva L.A. Differential algebra of biquaternions. 4. Twistors and twistor fields, Mathematical Journal, 13 (2013) 17-35 (in Russian).
7. Vladimirov V.S. Generalized functions in mathematical physics, Moscow, Nauka, 1978 (in Russian).
8. Handbook of mathematical functions with formulas, graphs and mathematical tables, Edited by M. Abramovitz, I.A. Stegun. National bureau of standard, Applied mathematics series-55, 1964.
9. Shilov G.E. Simple gamut, Moscow state university, 1970 (in Russian).
10. Alexeyeva L.A. Differential Algebra of Biquaternions. Dirac Equation and Its Generalized Solutions, Progress in Analysis. Proceedings of the 8-th Congress of the ISAAC, Moscow, 22-27 August, (2013), 153-161.
11. Lyudmila Alexeyeva Periodic system of atoms in biquaternionic representation, Journal of Modern Physics, 9:8 (2018), 1633-1644. https://doi.org/10.4236/jmp.2018.98102.
12. Alexeyeva L.A. Periodic system of atoms as simple gamma in biquaternionic representation, Scientific federation, Abstracts of 2nd International conference on Quantum Mechanics and Nuclear Engineering. Keynote forum. Paris, 23-24 September, (2019), P. 56.
