Self-sufficient potential formalism in describing electromagnetic interactions
DOI:
https://doi.org/10.3103/S0735272709120048Abstract
On the basis of interpreting Minkovskiy space-time as a distributed electromagnetic oscillating system an attempt to make potential formalism in electromagnetism theory to be self-sufficient (which does not require tensor of electromagnetic field) is described. Classification of the mentioned system is performed from the point of view of oscillations theory. A complete system of eigen functions of D’Alamber operand is built in a four-dimensional parallelepiped with respect to which the four-vector of electromagnetic potential is decomposed. Expressions for volume distributions of Lagrange function, energy and oscillating system’s pulse are obtained without tensor of electromagnetic field. Some physical consequences of applying the suggested mathematical approach are considered.
References
A. V. Gritsunov, “Expansion of Nonstationary Electromagnetic Potentials into Partial Functions of Electrodynamic System,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 49(7), 10 (2006); Radioelectron. Commun. Syst. 49(7), 7 (2006).
А. V. Veryovkina and А. V. Gritsunov, “To the theory of matrix methods of electrodynamics,” in Vestnik Dnepropetrovskogo universiteta. Fizika. Radioelektronika (Dnepropetrovsk University, Dnepropetrovsk, 2008), issue 15, No. 2/1, pp. 44–51.
A. V. Gritsunov and A. V. Veryovkina, “Matrix Electrodynamics: A Similarity to the Heisenberg’s Mechanics?,” in Proc. Ninth IEEE Int. Vacuum Electron Sources Conf. (IVEC 2008), Monterey, California, USA, 2008 (California, 2008), pp. 356–357.
L. D. Landau and Ye. М. Lifshitz, Field Theory (Nauka, Moscow, 1988) [in Russian].
R. Feynman, R. Leighton, and М. Sands, The Feynman Lectures on Physics, Vol. 6: Elektrodinamika (Addison-Wesley Publishing Company Inc., 1964; Mir, Moscow, 1977).
Ye. L. Feinberg, “On the special role of electromagnetic potentials in quantum mechanics,” Physics – Uspekhi, No. 9, 53 (1962).
А. V. Gritsunov, “Methods of calculating non-stationary non-harmonic fields in directing electrodynamic systems,” Radiotekh. Elektron., No. 6, 645 (2007).
L. I. Mandelstam, Full Collection of Works, Vol. IV: Lectures on Oscillations (Izdat. AN SSSR, Moscow, 1955) [in Russian].
V. B. Berestetskiy, Ye. М. Lifshitz, and L. P. Pitayevskiy, Quantum Electrodynamics (Nauka, Moscow, 1989) [in Russian].
L. D. Landau and Ye. М. Lifshitz, Theory of Elasticity (Nauka, Moscow, 1987) [in Russian].
G. Goldstein, Classical Mechanics (Nauka, Moscow, 1975) [in Russian].
