The vacuum structure, special relativity theory, and quantum mechanics: A return to the field theory approach without geometry

N. N. Bogolyubov (Jr.)   ; A. K. Prikarpatskii   ; U. Taneri

Teoretičeskaâ i matematičeskaâ fizika, Tome 160 (2009) no. 2, pp. 249-269

Résumé

We formulate the main fundamental principles characterizing the vacuum field structure and also analyze the model of the related vacuum medium and charged point particle dynamics using the developed field theory methods. We consider a new approach to Maxwell's theory of electrodynamics, newly deriving the basic equations of that theory from the suggested vacuum field structure principles; we obtain the classical special relativity theory relation between the energy and the corresponding point particle mass. We reconsider and analyze the expression for the Lorentz force in arbitrary noninertial reference frames. We also present some new interpretations of the relations between special relativity theory and quantum mechanics. We obtain the famous quantum mechanical Schrödinger-type equations for a relativistic point particle in external potential and magnetic fields in the semiclassical approximation as the Planck constant $\hbar\to0$ and the speed of light $c\to\infty$.

Détail

Keywords: vacuum structure, local mass conservation law, local momentum conservation law, relativity theory.
Mots-clés : Lorentz force

Bibliographie

[1] R. P. Feynman et al., (Based on notes by F. B. Morinigo and W. G. Wagner, edited by B. Hatfield), Addison-Wesley, Reading, MA, 1995

[2] P. G. de Gennes, Superconductivity of Metals and Alloys, Benjamin, New York, 1966 | Zbl

[3] J. Carstoiu, C. R. Acad. Sci. Paris, 268 (1969), 201–204

[4] M. A. Markov, “Printsip Makha i fizicheskii vakuum v obschei teorii otnositelnosti”, Problemy teoreticheskoi fiziki, Sbornik, posvyasch. 60-letiyu N. N. Bogolyubova, ed. D. I. Blokhintsev, Nauka, M., 1969, 26–27 | MR | Zbl

[5] E. F. Taylor, J. A. Wheeler, Spacetime Physics, Freeman, New York, 1992 | MR

[6] B. M. Barbashov, D. Blaschke, G. V. Efimov et al., Selected Problems of Modern Physics, Proc. of the XII-th Internat. Conf., Sect. 1, Dubna, 2003

[7] A. K. Prykarpatsky, N. N. Bogolubov Jr., The field structure of vacuum, Maxwell equations and relativity theory aspects. Part 1, arXiv: 0807.3691

[8] R. Feinman, R. Leiton, M. Sends, Feinmanovskie lektsii po fizike. T. 6. Elektrodinamika, Mir, M., 1977 | MR | MR | Zbl

[9] N. N. Bogolyubov, D. V. Shirkov, Vvedenie v teoriyu kvantovannykh polei, Nauka, M., 1973 | MR | MR | Zbl

[10] Dzh. D. Berken, S. D. Drell, Relyativistskaya kvantovaya teoriya. T. II. Relyativistskie kvantovye polya, Nauka, M., 1978 | MR | MR | Zbl

[11] A. I. Akhiezer, V. B. Berestetskii, Kvantovaya elektrodinamika, Nauka, M., 1981 | MR | MR | Zbl

[12] J. Schwinger, Quantum Electrodynamics, Dover, New York, 1958 | MR | Zbl

[13] I. Bialynicki-Birula, Phys. Rev., 155:5 (1967), 1414–1414 ; 166:5 (1968), 1505–1506 | DOI | MR | DOI

[14] A. Zommerfeld, Mekhanika, RKhD, Izhevsk, 2001 | Zbl

[15] L. Brillyuen, Novyi vzglyad na teoriyu otnositelnosti, Mir, M., 1972

[16] L. D. Faddeev, UFN, 136:3 (1982), 435–457 | DOI | MR | Zbl

[17] O. N. Repchenko, Polevaya fizika ili kak ustroen Mir?, Galeriya, M., 2005

[18] C. H. Brans, R. H. Dicke, Phys. Rev., 124:3 (1961), 925–935 | DOI | MR | Zbl

[19] A. A. Logunov, Lektsii po teorii otnositelnosti i gravitatsii, Nauka, M., 1987 | MR | MR | Zbl

[20] V. A. Fok, Teoriya prostranstva, vremeni i tyagoteniya, Nauka, M., 1961 | MR | Zbl

[21] V. Pauli, Teoriya otnositelnosti, Nauka, M., 1983 | MR | Zbl

[22] R. Weinstock, Amer. J. Phys., 33:8 (1965), 640–645 | DOI | Zbl

[23] A. R. Lee, T. M. Kalotas, Amer. J. Phys., 43:5 (1975), 434–437 | DOI

[24] J. M. Lévy-Leblond, Amer. J. Phys., 44:3 (1976), 271–277 | DOI

[25] N. D. Mermin, Amer. J. Phys., 52:2 (1984), 119–124 | DOI | MR

[26] A. Sen, Amer. J. Phys., 62:2 (1994), 157–162 | DOI | MR

[27] P. W. Bridgman, Reflections of a Physicist, Philosophical Library, New York, 1950 | Zbl

[28] A. Chorin, J. Marsden, A Mathematical Introduction to Fluid Mechanics, Texts Appl. Math., 4, Springer, New York, 1993 | DOI | MR | Zbl

[29] A. K. Prykarpatsky, N. N. Bogolubov (Jr.), J. Golenia, U. Taneri, Internat. J. Theoret. Phys., 47:11 (2008), 2882–2897 ; publications.ictp.it | DOI | MR | Zbl

[30] P. A. M. Dirak, Printsipy kvantovoi mekhaniki, Fizmatgiz, M., 1960 | MR | MR | Zbl

[31] V. A. Fock, Z. Phys., 75:9–10 (1932), 622–647 | DOI | Zbl

[32] F. A. Berezin, Metod vtorichnogo kvantovaniya, Nauka, M., 1965 | MR | Zbl

[33] A. K. Prykarpatsky, U. Taneri, N. N. Bogolubov Jr., Quantum Field Theory with Application to Quantum Nonlinear Optics, World Scientific, Singapore, 2002 | MR | Zbl

[34] A. Z. Petrov, Dokl. AN USSR, 190 (1970), 305

[35] Dzh. K. Maksvell, Traktat ob elektrichestve i magnetizme, T. 1, 2, Nauka, M., 1989 | MR | Zbl

[36] O. Heaviside, Electromagnetic Theory, V. I, The Electrician Printing, London, 1894 | Zbl

[37] L. Brillouin, R. Lucas, J. Phys. Radium, 27 (1966), 229–232 | DOI

[38] R. Burghardt, Acta Phys. Austr., 32 (1970), 272–281

[39] G. t'Hooft, Introduction to General Relativity, Rinton Press, Princeton, NJ, 2001 ; www.phys.uu.nl/~thooft/lectures/ genrel.pdf | MR | Zbl

[40] D. N. Mermin, It's About Time: Understanding Einstein's Relativity, Princeton Univ. Press, Princeton, NJ, 2005 | MR | Zbl

[41] B. M. Barbashov, V. V. Nesterenko, Model relyativistskoi struny v fizike adronov, Energoatomizdat, M., 1987 | MR | Zbl

[42] H. Collins, Gravity's Shadow: The Search for Gravitational Waves, University of Chicago Press, Chicago, 2004

[43] T. Damour, “General relativity and experiment”, XIth International Congress on Mathematical Physics, ed. D. Iagolnitzes, International Press, Cambridge, MA, 1995, 37–46 | MR | Zbl

[44] B. Green, The Elegant Universe. Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, Norton, New York, 1999 | MR | Zbl