Bel, Luis; Fustero, Xavier Mécanique relativiste predictive des systèmes de N particules. (French) Zbl 0347.35070 Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 25, 411-436 (1976). The authors reformulate the predictive relativistic mechanics of systems of \( \mathrm{N} \) particles in terms of integral or integrofunctional equations in accord with the approach of D. H i \( r \) on d e I [J. math. Phys. 15, 1689-1697 (1974)] in action-at-a-distance electrodynamics. They consider a slightly modified version of this technique and apply it to the following problems: (i) calculation of the Hamiltonian forms and generating functions of the associated canonical realization of the Poincaré group, (ii) integration of predictive Poincaré invariant systems, and (iii) the construction of predictive Poincaré invariant systems for scalar or vector interactions. This review text is based on a scanned copy of the printed version. It was converted to LaTeX using MathPix and a specifically developed LLM to assign the text parts to the metadata. It may contain errors, misassignments, or gaps; in particular, the reviewer signature has not yet been extracted reliably in general. If you notice any errors, please report them directly to our editorial team via the Contact Form. Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 Documents MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application × Cite Format Result Cite Review PDF Full Text: Numdam EuDML Geodesic References: [1] Ph. DROZ-VINCENT , Phys. Scripta , t. 2 , 1970 , p. 129 . MR 309506 | Zbl 1063.83553 · Zbl 1063.83553 · doi:10.1088/0031-8949/2/4-5/001 [2] L. Bel , Ann. Inst. H. Poincaré , t. 14 , 1971 , p. 189 . Numdam | MR 286379 [3] R. Arens , Arch. for Rat. Mech. and Analysis , t. 47 , 1972 , p. 255 . MR 347305 | Zbl 0244.70006 · Zbl 0244.70006 · doi:10.1007/BF00281634 [4] L. Bel et J. Martin , Ann. Inst. H. Poincaré , t. 22 , 1975 , p. 173 . Numdam | MR 378697 [5] L. Bel , Contribution dans Journées Relativistes ae Toulouse , 1974 . Université de Toulouse. Departement de Mathématiques . [6] L. Bel , Contribution au volume en l’honneur de A. Lichnerowicz (à paraître). [7] D. Hirondel , J. Math. Phys. , t. 15 , 1974 , p. 1689 . [8] L. Bel , A. Salas et J.M. Sanchez-Ron , Phys. Rev. D, t. 7 , 1973 , p. 1099 . [9] A. Salas et J.M. Sanchez-Ron , Il Nuovo Cimento , t. 20 B, 1974 , p. 209 . [10] X. Fustero , Tesis . Universidad Autonoma de Barcelona , 1974 . [11] L. Bel et J. Martin , C. R. Acad. Sc. , Paris , t. 277 , 1973 , p. 233 . MR 334799 [12] L. Bel et J. Martin , Phys. Rev. D , t. 9 , 1974 , p. 2760 . This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.