no. 4
Two-body relativistic systems
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 27 (1977) no. 4, pp. 407-424 
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     pages = {407--424},
     year = {1977},
     publisher = {Gauthier-Villars},
     volume = {27},
     number = {4},
     mrnumber = {496313},
     language = {en},
     url = {https://www.numdam.org/item/AIHPA_1977__27_4_407_0/}
}
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Droz-Vincent, Ph. Two-body relativistic systems. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 27 (1977) no. 4, pp. 407-424. https://www.numdam.org/item/AIHPA_1977__27_4_407_0/

[1] D.G. Currie, Journ. Math. Phys., t. 4, 1963, p. 1470; Phys. Rev., t. 142, 1966, p. 817. | Zbl

D.G. Currie, T.F. Jordan, E.C.G. Sudarshan, Rev. Mod. Phys., t. 35, 1963, p. 350. | MR

R.N. Hill, E.H. Kerner, Phys. Rev. Letters, t. 17, 1966, p. 1156. | Zbl

R.N. Hill, Journ. Math. Phys., t. 8, 1967, p. 1756; t. 11, 1970, p. 1918.

L. Bel, Ann. Inst. H. Poincaré, t. 3, 1970, p. 307. | MR | Numdam

[2] Ph. Droz-Vincent, Lett. Nuovo Cim., t. 1, 1969, p. 839; Physica Scripta, t. 2, 1970, p. 129. | Zbl

[3] J.G. Wray, Phys. Rev., t. D 1, n° 8, 1970, p. 2212.

[4] Ph. Droz-Vincent, Nuovo Cimento, t. 12 B, n° 1, 1972, p. 1. | MR

[5] Ph. Droz-Vincent, Lett. Nuovo Cim., t. 7, n° 6, 1973, p. 206.

[6] Ph. Droz-Vincent, Reports on Math. Phys., t. 8, n° 1, 1975, p. 79. | MR

[7] Our argument about it in ref. [4] is wrong, a term being omitted, thus its p. 8 is erroneous. However the theorem thereby stated in covariant form is true in the Poincaré invariant case. The correct proof is due to J. Martin (unpublished).

[8] Ph. Droz-Vincent, Hamiltonian Construction of Predictive Systems. Book in the honor of A. Lichnerowicz, Cahen and Flato, ed. D. Reidel, Dordrecht, 1977. | Zbl | MR

[9] Recall that, even in classical mechanics, the positions are H-J-coordinates only in the free case.

[10] L. Bel, J. Martin, Ann. Inst. H. Poincaré, t. XXII, n° 3, 1975, p. 173. In this paper they have introduced H-J-coordinates in Predictive Mechanics. | MR | Numdam

[11] Landau-Lifshitz, The classical Theory of Fields, Chap. 2, p. 39, Pergamon. | Zbl

[12] Ph. Droz-Vincent, C. R. Acad. Sc. Paris, t. 280 A, 1975, p. 1169. | MR

[13] A different generalization is considered in ref. [8].

[14] Ph. Droz-Vincent, C. R. Acad. Sc. Paris, t. 282 A, 1976, p. 727.

[15] See for instance: H. Bacry, H. Ruegg, J.M. Souriau, Comm. Math. Phys., t. 3, 1966, p. 323. | Zbl

[16] In contrast with our point of view, some authors have introduced quantum relativistic oscillators by wave equations which are not derived from a classical system by the procedure of quantization:

Y.S. Kim, M.E. Noz, Phys. Rev., t. D 12, 1975, p. 129; t. D 12, 1975, p. 122.

Y.S. Kim, S.H. Oh, Preprint, 1976.

J.F. Gunion, L.F. Li, Phys. Rev., t. D 12, n° 11, 1975, p. 3583.