Relativistic model of interatomic interactions
https://doi.org/10.34680/2076-8052.2023.5(134).727-734
Abstract
In this paper, we propose a method for relativistic description of the dynamics of systems of interacting particles through an auxiliary field which in the static mode is equivalent to given interatomic potentials, and in the dynamic mode is a classical relativistic field. It has been established that for static interatomic potentials of a general form, the auxiliary field is a composition of elementary fields satisfying the Klein-Gordon type equations. Each elementary field is characterized by a complex parameter which is an analogue of the real mass in the Klein-Gordon equation. The interaction between particles through an auxiliary field is nonlocal both in spatial variables and in time. The qualitative properties of solutions to equations describing the auxiliary field are studied. Relativistic mechanisms of both the thermodynamic behavior and synergetic effects in few-particle systems have been established.
About the Authors
A. Yu. Zakharov
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
M. A. Zakharov
Yaroslav-the-Wise Novgorod State University
Russian Federation
Russian Federation
Veliky Novgorod
References
1. Ares de Parga G., López-Carrera B. Relativistic Statistical Mechanics vs. Relativistic Thermodynamics // Entropy. 2011. 13(9). 1664-1693. DOI: 10.3390/e13091664
2. Lusanna L. From Relativistic Mechanics towards Relativistic Statistical Mechanics // Entropy. 2017. 19(9). 436. DOI: 10.3390/e19090436
3. Tolman R. C. Thermodynamics and relativity // Bulletin of the American Mathematical Society. 1933. 39(2). 49-74. DOI: 10.1090/S0002-9904-1933-05559-3
4. Ott H. Lorentz-Transformation der Wärme und der Temperatur // Zeitschrift für Physik. 1963. 175(1). 70-104. DOI: 10.1007/BF01375397
5. Nakamura T. K. Three Views of a Secret in Relativistic Thermodynamics // Progress of Theoretical Physics. 2012. 128(3). 463-475. DOI: 10.1143/PTP.128.463
6. ter Haar D., Wergeland H. Thermodynamics and statistical mechanics in the special theory of relativity // Physics Reports. 1971. 1(2). 31-54. DOI: 10.1016/0370-1573(71)90006-8
7. de Groot S. R., van Leeuwen W. A., van Weert Ch. G. Relativistic Kinetic Theory: Principles and Applications. New York, North-Holland Pub. Co., 1980. 417 p.
8. Trump M. A., Schieve W. C. Classical Relativistic Many-Body Dynamics. Dordrecht, Springer, 1999. 375 p.
9. Cercignani C., Kremer G.M. The Relativistic Boltzmann Equation: Theory and Applications. Basel, Birkhäuser, 2002. 394 p.
10. Liboff R. Kinetic Theory: Classical Quantum and Relativistic Descriptions. New York, Springer, 2003. 587 p.
11. Hakim R. Introduction to Relativistic Statistical Mechanics: Classical and Quantum. New Jersey, World Scientific, 2011. 566 p.
12. Newton R. G. From Clockwork to Crapshoot: A History of Physics; Harvard University Press, London, UK, 2007. P. 179.
13. Ulam S. M. Zur Maßtheorie in der allgemeinen Mengenlehre // Fundamenta Mathematicae. 1930. 16(2). 140-150. DOI: 10.4064/fm-16-1-140-150
14. Khrennikov A. Yu. Interpretations of probability / 2nd rev. and extended ed. Berlin, Walter de Gruyter, 2009. 217 p.
15. Khrennikov A. Yu. Probability and Randomness: Quantum Versus. London, Imperial College Press, 2016. 282 p.
16. Currie D. G. Interaction contra classical relativistic Hamiltonian particle mechanics ie // Journal of Mathematical Physical. 1963. 4(12). 1470-1488. DOI: 10.1063/1.1703928
17. Currie D. G., Jordan T. F., Sudarshan E. C. G. Relativistic invariance and Hamiltonian theories of interacting particles // Revitws of Modern Physics. 1963. 35(2). 350-375. DOI: 10.1103/RevModPhys.35.350
18. Leutwyler H. A no-interaction theorem in classical relativistic Hamiltonian particle mechanics // Nuovo Cimento. 1965. 37(2). 556-567. DOI: 10.1007/BF02749856
19. Zakharov A. Y., Zubkov V. V. Field Form of the Dynamics of Classical Manyand Few-Body Systems: From Microscopic Dynamics to Kinetics, Thermodynamics and Synergetics // Quantum Reports. 2022. 4(4). 533-543. DOI: 10.3390/quantum4040038
20. Zakharov A. Y., Zubkov V. V. Field-Theoretical Representation of Interactions between Particles: Classical Relativistic Probability-Free Kinetic Theory // Universe. 2022. 8(5). 281. DOI: 10.3390/universe8050281
21. Ali A., Kramer G. Jets and QCD: a historical review of the discovery of the quark and gluon jets and its impact on QCD // The European Physical Journal H. 2011. 36(2). 245-326. DOI: 10.1140/epjh/e2011-10047-1
22. Sazdjian H. The Interplay between Compact and Molecular Structures in Tetraquarks // Symmetry. 2022. 14. 515. DOI: 10.3390/sym14030515
23. Loktionov I. K. Application of two-parameter oscillating interaction potentials for specifying the thermophysical properties of simple liquids // High Temptrature. 2012. 50(6). 708-716. DOI: 10.1134/S0018151X12050094
24. Loktionov I. K. Studying equilibrium thermophysical properties of simple liquids based on a four-parameter oscillating interaction potentiaL // High Temperature. 2014. 52(3). 390-402. DOI: 10.1134/S0018151X14020151
25. Lorenz L. On the identity of the vibrations of light with electrical currents // The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1867. 34(230). 287-301. DOI: 1080/14786446708639882
26. Riemann B. A contribution to electrodynamics // The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 1867. 34(231). 368-372. DOI: 10.1080/14786446708639897
27. Zakharov A. Y., Zakharov M. A. Microscopic Dynamic Mechanism of Irreversible Thermodynamic Equilibration of Crystals // Quantum Reports. 2021. 3(4). 724-730. DOI: 10.3390/quantum3040045
Review
For citations:
Zakharov A.Yu., Zakharov M.A. Relativistic model of interatomic interactions. Title in english. 2023;(5(134)):727-734. (In Russ.) https://doi.org/10.34680/2076-8052.2023.5(134).727-734
Views:
24
Email this article 