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Reference8 articles.
1. There have been many works on the relativistic 2-body (orN-body) scattering. Apart from the schemes strongly connected with field theory, there has been some proposal for dealing directly and covariantly with a « potential»; seeC. Fronsdal andL. E. Lundberg:Phys. Rev. D,1, 3247 (1970);P. Cordero, C. Fronsdal andT. Gajdicar:Phys. Rev. D,5, 2002 (1972);L. Bel:Volume in the Honor of A. Lichnerowicz, edited byM. Cahen andM. Flato (Dordrecht, 1977);J. M. Namysłowski:Phys. Rev. D,18, 3676 (1978). The latter follows the lines of constrained relativistic dynamics according toI. T. Todorov: Report No. JINR E2-10125, Dubna, 1976 (unpublished); a relationship with our multitime approach is likely to exist. But, even at the nonquantum level, the correspondence remains to be carefully clarified.
2. Ph. Droz-Vincent:Phys. Scr.,2, 129 (1970);Rep. Math. Phys.,8, 79 (1975);Ann. Inst. Henri Poincaré,27, 407 (1977). The formula giving dσ a /dτ a is explained inPh. Droz-Vincent:Volume in the Honor of A. Lichnerowicz, edited byM. Cahen andM. Flato (Dordrecht, 1977);N-body relativistic systems, preprint (1979) (to appear inAnn. Inst. Henri Poincaré).
3. Ph. Droz-Vincent:Lett. Nuovo Cimento,1, 800 (1971);Rep. Math. Phys.,8, 79 (1975);Phys. Rev. D,19, 702 (1979).
4. Whenf is solution of (1), it is not inL 2. But it is easy to legitimate (5)-(7) in this case whereU acts like a numerical factor. When we consider off-shell states, (5) and (7) hold inL 2, (6) is no longer true. Equation (5) is theN-body generalization of a relativistic Schrödinger equation first written by Stückelberg:E. C. G. Stückelberg:Helv. Phys. Acta,14, 588 (1941);15, 23 (1948).
5. J. M. Jauch:Helv. Phys. Acta,31, 127 (1958).
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