Abstract:
Relativistic invariance is shown to be violated in the transition to the classical limit
according the usual rule of Wigner and Moyal. A modification of the limiting procedure,
which restores the relativistic invariance, is proposed. With the aid of this procedure
3 solutions of the Dirac problem of the classical relativistic hamiltonian description of
directly interacting particles are found for the simplest case of two one-dimensional
particles.
Citation:
S. N. Sokolov, “Is relativistic invariance preserved in the limit ℏ→0?”, TMF, 32:3 (1977), 354–359; Theoret. and Math. Phys., 32:3 (1977), 790–794
\Bibitem{Sok77}
\by S.~N.~Sokolov
\paper Is relativistic invariance preserved in the limit $\hbar\to 0$?
\jour TMF
\yr 1977
\vol 32
\issue 3
\pages 354--359
\mathnet{http://mi.mathnet.ru/tmf3171}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=462348}
\transl
\jour Theoret. and Math. Phys.
\yr 1977
\vol 32
\issue 3
\pages 790--794
\crossref{https://doi.org/10.1007/BF01089562}
Linking options:
https://www.mathnet.ru/eng/tmf3171
https://www.mathnet.ru/eng/tmf/v32/i3/p354
This publication is cited in the following 5 articles:
S. N. Sokolov, V. I. Tretyak, “Front form of relativistic Lagrangian dynamics in two-dimensional space-time and its connection with the Hamiltonian description”, Theoret. and Math. Phys., 67:1 (1986), 385–394
S. N. Sokolov, “Coordinates in relativistic Hamiltonian mechanics”, Theoret. and Math. Phys., 62:2 (1985), 140–148
R. P. Gaida, Yu. B. Klyuchkovskii, V. I. Tretyak, “Lagrangian classical relativistic mechanics of a system of directly interacting particles. I”, Theoret. and Math. Phys., 44:2 (1980), 687–697
S. N. Sokolov, “Relativistic addition of direct interactions in the point form of dynamics”, Theoret. and Math. Phys., 36:2 (1978), 682–692
S. N. Sokolov, A. N. Shatnii, “Physical equivalence of the three forms of relativistic dynamics and addition of interactions in the front and instant forms”, Theoret. and Math. Phys., 37:3 (1978), 1029–1038
Citation in format AMSBIB
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