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The S-matrix in classical mechanics. (English) Zbl 0159.55001

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[1] After this was written, we learned thatJ. M. Cook had already treated the caseN=2 in the same spirit (see 1965 Cargèse Lectures in Theoretical Physics, edited byF. Lurcat. New York: Gordon & Breach 1967).
[2] Kato, T.: Trans. Am. Math. Soc.70, 195 (1951).
[3] Nelson, E.: Operator differential equations, Lemma 12.1, mimeographed lecture notes. Princeton University 1964.
[4] Ruelle, D., unpublished.
[5] Essentially we followJauch, J. M., Helv. Physica Acta31, 661 (1958), but we prefer a different definition of theS-operator, due toBerezin, F. A., L. D. Faddeev, andR. A. Minlos, Proceedings of the Fourth All-Union Mathematical Conference, held in Leningrad 1961.
[6] This is a classical result: seeSiegel, C. L.: Vorlesungen über Himmelsmechanik, § 30, Berlin, Göttingen, Heidelberg: Springer 1956. I am indebted toR. Jost for this remark.
[7] For the quantum mechanical proof seeHack, M. N.: Nuovo Cimento13, 231 (1959). · Zbl 0086.42804 · doi:10.1007/BF02727547
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