Two-body relativistic systems in external field
Annales de l'I.H.P. Physique théorique, Tome 50 (1989) no. 2, pp. 187-204.
@article{AIHPA_1989__50_2_187_0,
     author = {Droz-Vincent, Philippe},
     title = {Two-body relativistic systems in external field},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {187--204},
     publisher = {Gauthier-Villars},
     volume = {50},
     number = {2},
     year = {1989},
     mrnumber = {1002819},
     zbl = {0671.70008},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1989__50_2_187_0/}
}
TY  - JOUR
AU  - Droz-Vincent, Philippe
TI  - Two-body relativistic systems in external field
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1989
SP  - 187
EP  - 204
VL  - 50
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1989__50_2_187_0/
LA  - en
ID  - AIHPA_1989__50_2_187_0
ER  - 
%0 Journal Article
%A Droz-Vincent, Philippe
%T Two-body relativistic systems in external field
%J Annales de l'I.H.P. Physique théorique
%D 1989
%P 187-204
%V 50
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPA_1989__50_2_187_0/
%G en
%F AIHPA_1989__50_2_187_0
Droz-Vincent, Philippe. Two-body relativistic systems in external field. Annales de l'I.H.P. Physique théorique, Tome 50 (1989) no. 2, pp. 187-204. http://www.numdam.org/item/AIHPA_1989__50_2_187_0/

[1] Relativistic Action-at-a-Distance Classical and Quantum Aspects. Lecture Notes in Physics, n° 162, J. Llosa Editor, Springer Verlag, 1982, and references therein. | MR

[2] Ph. Droz-Vincent, Reports on Mathematical Physics, t. 8, n° 1, 1975, p. 79. | MR

[3] Ph. Droz-Vincent, Phys. Rev., t. D 19, 1979, p. 702. | MR

[4] H. Leutwyler, J. Stern, Ann. Phys. (N.-Y.), t. 112, 1978, p. 94. Phys. Lett., t. B73, 1978, p. 75. | MR

[5] I.T. Todorov, J. I. N. R. Report E2-10125, Dubna, 1976, and contribution to Ref. 1,

[6] L. Bel, In Differential Geometry and Relativity, M. Cahen and M. Flato Editors, Reidel-Dordrecht, 1976; Phys. Rev., t. D 28, 1983, p. 1308. | MR

[7] H. Crater and P. Van Alstine, Ann. Phys. (N-Y), t. 148, 1983, p. 1308 ; Phys. Rev., t. D 30, 1984, p. 2585. | MR

[8] Ph. Droz-Vincent, Nuovo Cimento, t. 58 A, 1980, p. 355.

[9] Ph. Droz-Vincent, Phys. Rev., t. D 29, 1984, p. 687. Beware that (in contrast to Ref. 8) the convention made in this article is pa = - i∂a, thus the phase in the evolution operators U, U has been choosen with the wrong sign which amounts to exchange in and out - states, Ω+ and Ω-, S and S*. This does not affect the results of this paper (invariance of mass-shell, unitarity, etc.) but should be taken into account in case of a practical application. | MR

[10] L.P. Horwitz, F. Rohrlich, Phys. Rev., t. D 24, 1981, p. 1528 ; t. 26, 1982, p. 3452.

[11] V.A. Rizov, H. Sazdjian, I.T. Todorov, Ann. of Phys., t. 165, 1985, p. 59. | MR

[12] Ph. Droz-Vincent, Ann. Inst. H. Poincaré, t. A 27, 1977, p. 407. | Numdam | MR

[13] V.V. Molotkov, I.T. Todorov, Comm. Math. Phys., t. 79, 1981, p. 111. | MR

[14] J. Martin, J.L. Sanz, Ann. Inst. H. Poincaré, t. 24, n° 4, 1976, p. 347. | Numdam

[15] S.N. Sokolov, Theor. Math. Phys., t. 36, 1979, p. 682; Theor. Math. Phys., t. 37, 1979, p. 1029.

[16] Ph. Droz-Vincent, Ann. Inst. H. Poincaré, t. A 32, 1980, p. 377. | Numdam | MR

[17] H. Sazdjian, Lett. Math. Phys., t. 5, 1981, p. 319. | MR

[18] S.I. Bidikov, I.T. Todorov, Lett. Math. Phys., t. 5, 1981, p. 461. | MR

[19] F. Rorhlich, Phys. Rev., t. D 23, 1981, p. 1305.

[20] T. Biswas, F. Rohrlich, Lett. Math. Phys., t. 6, 1982, p. 325. | MR

[21] Ph. DROZ-VINCENT, Lett. Nuov. Cimento, t. 1, 1969, p. 839 ; Physica Scripta, t. 2, 1970, p. 129 and Refs. [2], [3], [12]. R. Arens, Archiv. Rat. Mech. Analy., t. 47, 1972, p. 255. L. BEL, Ann. Inst. H. Poincaré, t. 3, 1970, p. 307, and Ref. [6].

[22] L. Lusanna, Nuovo Cimento, t. 65 B, 1981, p. 135. | MR

[23] D. Dominici, J. Gomis, J.A. Lobo, J.M. Pons, Nuovo Cim., t. B 61, 1981, p. 306.

[24] J. Bijtebier, to appear in « Few Body Systems », t. 3, 1987, p. 41.

[25] The quantized version of the oscillator considered in Ref. [12] is finally equivalent to the one given by Y.S. Kim and M.E. Noz, Phys. Rev., t. D 12, 1975, p. 122 and 129. See Ref. [28] below.

[26] Ph. Droz-Vincent, Lett. Nuovo Cim., t. 30, 1981, p. 375. | MR

L. Bel, Phys. Rev., t. D, 1983, p. 1308.

[27] Alternatively, the use of Weyl spinors with a pair of coupled Feynman-Gell-Mann equations seems to open new simplifications.

Ph. Droz-Vincent, Phys. Letters, t. A 120, 1987, p. 313. | MR

[28] A.A. Logunov, A.N. Tavkhelidze, Nuovo Cim., t. 29, 1963, p. 380.

A.A. Logunov, A.N. Tavkhelidze, I.T. Todorov, O.A. Khrustalev, Nuovo Cim., t. 30, 1963, p. 134.

V.A. Rizov, I.T. Todorov, B.L. Aneva, Nuclear Physics, t. B 98, 1975, p. 447.

[29] V. Iranzo, J. Llosa, F. Marques, A. Molina, Ann. Inst. H. Poincaré, t. 40, 1984, p. 1.

[30] From a purely axiomatic point of view the concept of « free » system is rather flexible. This is made clear for instance in W. O. Amrein, Non-Relativistic Quantum Dynamics, Mathematical Physics Studies n° 2, Reidel-Dordrecht, 1981, chap. 5, p. 125.

[31] Y. Thiry, Les Fondements de la Mécanique Céleste, Gordon and Breach, London, 1970, chap. IV, p. 151-152. | Zbl

We notice that the spring constant is not a first integral, but simply a parameter. According to Lagrange method it is not supposed to vary.

[32] I.T. Todorov, Contribution to Ref. [1] and also the last Ref. [27].

A.O. Barut, J. Kraus, J. Math. Phys., t. 17, 1976, p. 506. | MR

A.O. Barut, J. Math. Phys., t. 21, 1980, p. 568. | MR