@article{AIHPA_1980__32_4_377_0, author = {Droz-Vincent, Ph.}, title = {N-body relativistic systems}, journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique}, pages = {377--389}, publisher = {Gauthier-Villars}, volume = {32}, number = {4}, year = {1980}, mrnumber = {594636}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1980__32_4_377_0/} }
TY - JOUR AU - Droz-Vincent, Ph. TI - N-body relativistic systems JO - Annales de l'institut Henri Poincaré. Section A, Physique Théorique PY - 1980 SP - 377 EP - 389 VL - 32 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1980__32_4_377_0/ LA - en ID - AIHPA_1980__32_4_377_0 ER -
Droz-Vincent, Ph. N-body relativistic systems. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Volume 32 (1980) no. 4, pp. 377-389. http://www.numdam.org/item/AIHPA_1980__32_4_377_0/
[1] An exhaustive list of references is by now impossible. See for instance
J. Math. Phys., t. 8, 1967, p. 201.
,Phys. Rev., t. D 1, n° 8, 1970, p. 2212.
,Ann. Inst. Henri Poincaré, t. 12, 1970, p. 307. | Numdam | MR
,Arch. for Rat. Mech. and Analysis, t. 47, 1972, p. 255. | MR | Zbl
,Phys. Rev., t. D 4, 1971, p. 1689.
,Phys. Rev., t. D 3, 1971, p. 2351.
,Nucl. Phys., t. B 133, 1978, p. 115.
and ,Prog. Theor. Phys., t. 54, n° 2, 1975, p. 563.
,Nuovo Cimento, t. 48 A, 1978, p. 257; Nuovo Cimento, t. 48 B, 1978, p. 152.
, , ,And also references [2-4] and [8].
Quoted below.
[2] Lett. Nuovo Cim., t. 1, 1969, p. 839; Physica Scripta, t. 2, 1970, p. 129. | Zbl
,[3] Reports on Math. Phys., t. 8, n° 1, 1975, p. 79. | MR
,[4] Ann. Inst. Henri Poincaré, t. 27, 1977, p. 407. | Numdam | MR
,[5] Phys. Letters, t. 68 B, 1977, p. 239.
and ,Progr. Theor. Phys., t. 57, 1977, p. 331; t. 58, 1977, p. 1229; D. P. N. U. Report 15-78, 1978.
,Phys. Rev., t. D 18, n° 8, 1978.
,[6] Ann. Inst. Henri Poincaré, t. 24, 1976, p. 411. See also
and ,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.
,[7] The spirit of our formulation is similar to that of 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.
,[8] J. Math. Phys., t. 4, 1963, p. 1470; Phys. Rev., t. 142, 1966, p. 817. | MR | Zbl
,Rev. Mod. Phys., t. 35, 1963, p. 350. | MR
, and ,Nuovo Cim., t. 37, 1965, p. 556.
,[9] C. R. Acad. Sc. Paris, t. A 182, 1979.
,[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).
[11] Lett. Nuovo Cim., t. 23, n° 5, 1978, p. 184. | MR
,[12] Phys. Rev., t. D 19, n° 2, 1979, p. 702. | MR
,[13] Note that the sign of the potential depends on the space time signature.
[14] For N = 2, see for example:
Plays. Rev., t. D 3, 1971, p. 2706.
, and ,Phys. Rev., t. D 15, 1977, p. 335.
and ,Phys. Rev., t. D 12, 1975, p. 3583.
and ,Phys. Rev., t. D 16, 1977, p. 1580. For N = 3, see ref. [5].
,[15] Note that abandoning the single-potential assumption will only introduce interaction terms in the « subsidiary » equations (4.6).