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Formulae for Energy and Momentum of Relativistic Particle Regular at Zero-Mass State
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Journal of Modern Physics·Volume 02 (2011)·Pages 849–856·Published 8 August 2011·DOI10.4236/jmp.2011.28101
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Abstract
In this paper we substantiate a necessity of introduction of a concept <i>the counterpart of rapidity</i> into the framework of relativistic physics. It is shown, formulae for energy and momentum defined via counterpart of rapidity are regular near the zero-mass and speed of light states. The representation for the energy-momentum is realized as a mapping from the massless-state onto the massive one which looks like as a "q"-deformation. Quantization of the energy, momentum and the velocity near the light-speed is presaged. An analogue between the relativistic dynamics and the statistical thermodynamics of a micro-canonical ensemble is brought to light.
KeywordsRelativistic DynamicsComplex AlgebraRapidityEnergy-MomentumBackground EnergyStatistical Thermodynamics.
- W. Heisenberg, “Zur Theorie de Elementarteilchen,” Zeit Naturforsch, Vol. 14a, 1959, pp. 441-451.
- Y. Nambu, “Dynamical Model of Elementary Particles Based on an Anal-ogy with Superconductivity,” Physical Review, Vol. 117, 1960, pp. 648-659. doi:10.1103/PhysRev.117.648
- J.-M. Levy-Leblond, “A Gedankenexperiment in Science History,” American Journal of Physics, Vol. 48, 1980, pp. 345-354.
- V. Varicak, “Ap-plication of Lobachevskian Geometry in the Theory of Relativ-ity,” Physikalische Zeitschrift, Vol. 11, 1910, pp. 93-96.
- H. Hergoltz, “Geometrical Aspects of Relativity Theory,” Ann.d.Phys, Vol.10, 1910, pp. 31-45.
- A. A. Robb, “Optical Geometry of Motion, a New View of the The-ory of Relativity,” Cambridge, 1911.
- A. A. Ungar, “Hy-perbolic Trigonometry and Its Applications in Poincaré Ball Model of Hyperbolic Geometry,” Computers & Mathematics with Applications, Vol. 41, No. 1-2, 2001, pp. 135-147. doi:10.1016/S0898-1221(01)85012-4
- A. O. Barut, “Elec-trodynamics and Classical Theory of Fields and Particles,” Dover Publications, Inc., New York, 1980.
- R. M. Ya-maleev, “Extended Relativistic Dynamics of Charged Spinning Particle in Quaternionic Formulation,” Advances in Applied Clifford Algebras, Vol. 13, No. 2, 2003, pp. 183-218. doi:10.1007/s00006-003-0015-8
- R. M. Yamaleev, “Rela-tivistic Equations of Motion within Nambu’s Formalism of Dy-namics,” Annals of Physics, Vol. 285, No. 2, 2000, pp. 141-160. doi:10.1006/aphy.2000.6075
- A. R. Rodriguez-Dominguez, “Ecuaciones de fuerza de Lorentz Como Ecuaciones de Heisenberg,” Revista Mexicana de Fisica, Vol. 53, No. 4, 2007, pp. 270-280.
- I. M. Yaglom, “Complex Numbers in Ge-ometry,” Academic Press, New York, 1968.
- P. Fjelstad and S. Gal, “Two Dimensional Geometries, Topologies, Trigo-nometries and Physics Generated by Complex-Type Numbers,” Advances in Applied Clifford Algebras, Vol. 11, No. 1, 2001, pp. 81-90. doi:10.1007/BF03042040
- R. M. Yamaleev, “Multicom-plex Algebras on Polynomials and Generalized Hamilton Dy-namics,” Journal of Ma- thematical Analysis and Applications, Vol. 322, No. 2, 2006, pp. 815-824. doi:10.1016/j.jmaa.2005.09.073
- R. M. Yamaleev, “Geo-metrical and Physical Interpretation of Evolution Governed by General Complex Algebra,” Journal of Mathematical Analysis and Application, Vol. 340, No. 2, 2008, pp. 1046-1057. doi:10.1016/j.jmaa.2007.09.018