Is relativistic invariance preserved in the limit $\hbar\to 0$?
Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 3, pp. 354-359 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
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S. N. Sokolov. Is relativistic invariance preserved in the limit $\hbar\to 0$?. Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 3, pp. 354-359. http://geodesic.mathdoc.fr/item/TMF_1977_32_3_a5/

[1] E. P. Wigner, Phys. Rev., 40 (1932), 479 | DOI

[2] J. E. Moyal, Proc. Cambr. Phil. Soc., 45 (1949), 99 | DOI | MR | Zbl

[3] Yu. M. Shirokov, TMF, 25 (1975), 307 ; 28 (1976), 308 | Zbl | Zbl

[4] B. Bakamjian, L. H. Thomas, Phys. Rev., 92 (1953), 1300 | DOI | MR | Zbl

[5] T. F. Jordan, A. J. Macfarlane, E. C. G. Sudarshan, Phys. Rev., 133B (1964), 487 | DOI | MR

[6] F. Coester, Helv. Phys. Acta, 38 (1965), 7 ; “Meson theory of nuclear forces”, Quanta, Univ. of Chicago Press, 1970, 147–165 | MR | Zbl

[7] S. N. Sokolov, TMF, 18 (1974), 56 | MR

[8] S. N. Sokolov, DAN SSSR, 221 (1975), 809 | MR

[9] P. A. M. Dirac, Rev. Mod. Phys., 21 (1949), 392 | DOI | MR | Zbl

[10] L. Cohen, J. Math. Phys., 7 (1966), 781 ; 17 (1976), 1863 | DOI | MR | DOI