N-body relativistic systems

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1. [1] An exhaustive list of references is by now impossible. See for instance 
2. R.N. Hill, J. Math. Phys., t. 8, 1967, p. 201. 
3. J.G. Wray, Phys. Rev., t. D 1, n° 8, 1970, p. 2212. 
4. L. Bel, Ann. Inst. Henri Poincaré, t. 12, 1970, p. 307. MR266567
5. R. Arens, Arch. for Rat. Mech. and Analysis, t. 47, 1972, p. 255. Zbl0244.70006MR347305
6. C. Fronsdal, Phys. Rev., t. D 4, 1971, p. 1689. 
7. I.T. Todorov, Phys. Rev., t. D 3, 1971, p. 2351. 
8. H. Leutwyler and J. Stern, Nucl. Phys., t. B 133, 1978, p. 115. 
9. T. Takabayashi, Prog. Theor. Phys., t. 54, n° 2, 1975, p. 563. 
10. D. Dominici, J. Gomis, G. Longhi, Nuovo Cimento, t. 48 A, 1978, p. 257; Nuovo Cimento, t. 48 B, 1978, p. 152. 
11. And also references [2-4] and [8]. 
12. Quoted below. 
13. [2] Ph. Droz-Vincent, Lett. Nuovo Cim., t. 1, 1969, p. 839; Physica Scripta, t. 2, 1970, p. 129. Zbl1063.83553
14. [3] Ph. Droz-Vincent, Reports on Math. Phys., t. 8, n° 1, 1975, p. 79. MR418156
15. [4] Ph. Droz-Vincent, Ann. Inst. Henri Poincaré, t. 27, 1977, p. 407. MR496313
16. [5] G. Preparata and K. Szego, Phys. Letters, t. 68 B, 1977, p. 239. 
17. T. Takabayachi, Progr. Theor. Phys., t. 57, 1977, p. 331; t. 58, 1977, p. 1229; D. P. N. U. Report 15-78, 1978. 
18. H.W. Crater, Phys. Rev., t. D 18, n° 8, 1978. 
19. [6] L. Bel and X. Fustero, Ann. Inst. Henri Poincaré, t. 24, 1976, p. 411. See also 
20. L. Bel, Phys. Rev., t. D 18, n° 12, 1979, p. 4770. In their case, classical field theory automatically provides N-body difference-differential equations, as usual. Then they reduce these equations to a predictive differential system by a series expansion method. In our case one wishes to ignore field theory from the outset. 
21. [7] The spirit of our formulation is similar to that of P.A.M. Dirac, Commun. Dublin Inst. Adv. Studies, A, n° 2, 1943. But of course we take into account the facts implied by Currie's No-Go Theorem. 
22. [8] D.G. Currie, J. Math. Phys., t. 4, 1963, p. 1470; Phys. Rev., t. 142, 1966, p. 817. Zbl0125.19505MR158737
23. D.G. Currie, T.F. Jordan and E.C.C. Sudarshan, Rev. Mod. Phys., t. 35, 1963, p. 350. MR151138
24. H. Leutwyler, Nuovo Cim., t. 37, 1965, p. 556. 
25. [9] Ph. Droz-Vincent, C. R. Acad. Sc. Paris, t. A 182, 1979. 
26. [10] Trivial for a single particle. For N = 2 see ref. [4] and DROZ-VINCENT, in Volume in the honor of A. Lichnerowicz, Cahen and Flato, Ed. D. Reidel, Dordrecht. The argument holds for any N. It is based upon the « individuality » property expressed in eq. (1.4). 
27. [11] Ph. Droz-Vincent, Lett. Nuovo Cim., t. 23, n° 5, 1978, p. 184. MR522824
28. [12] Ph. Droz-Vincent, Phys. Rev., t. D 19, n° 2, 1979, p. 702. MR518731
29. [13] Note that the sign of the potential depends on the space time signature. 
30. [14] For N = 2, see for example: 
31. R.P. Feynman, M. Kislincer and R. Ravndal, Plays. Rev., t. D 3, 1971, p. 2706. 
32. Y.S. Kim and M.L. Noz, Phys. Rev., t. D 15, 1977, p. 335. 
33. J.F. Gunion and L.F. Li, Phys. Rev., t. D 12, 1975, p. 3583. 
34. H.W. Crater, Phys. Rev., t. D 16, 1977, p. 1580. For N = 3, see ref. [5]. 
35. [15] Note that abandoning the single-potential assumption will only introduce interaction terms in the « subsidiary » equations (4.6). 

1. A. K. Pogrebkov, I. T. Todorov, Relativistic hamiltonian dynamics of singularities of the Liouville equation