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Low's Scattering Equation for the Charged and Neutral Scalar Theories

L. Castillejo* and R. H. Dalitz†

F. J. Dyson

  • Laboratory of Nuclear Studies, Cornell University, Ithaca, New York

  • Institute for Advanced Study, Princeton, New Jersey

  • *Supported by a fellowship from the Foreign Operations Administration. Now at the Physics Department, University College, London, England.
  • †Now at the Mathematical Physics Department, University of Birmingham, Birmingham, England. This work was completed while the second author was Visiting Associate Physicist at the Brookhaven National Laboratory.
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Phys. Rev. 101, 453 – Published 1 January, 1956

DOI: https://doi.org/10.1103/PhysRev.101.453

Abstract

The Low scattering equation is studied in the one-meson approximation with both charged and neutral scalar meson theories. The general solution is found for each of these cases. It has the general character of a Wigner-Eisenbud dispersion formula and contains an infinite number of adjustable parameters. It follows that the Low equation, in this approximation at least, does not determine the scattering, but only expresses a property of the scattering which is independent of the internal structure of the scatterer.

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References (11)

  1. F. E. Low, Phys. Rev. 97, 1392 (1955)
  2. Dr. Lee for an unpublished communication on this subject
  3. Low's [1]
  4. E. P. Wigner, Ann. of Math. 53, 36 (1951) [E. P. Wigner and J. v. Neumann, Ann. Math. 59, 418 (1954)], [10]
  5. J. A. Shohat and J. D. Tamarkin, The Problem of Moments (American Mathematical Society, New York, 1943)
  6. P. I. Richards, Quart. J. Appl. Math. 6, 21 (1948)
  7. A. Herglotz, Ber. Verhandl. sachs. Akad. Wiss. Leipzig, Math. naturw. Kl. 63 (1911)

  8. Omitted endnote

  9. Dr. F. E. Low (private communication)
  10. E. P. Wigner and L. Eisenbud, Phys. Rev. 72, 29 (1947)
  11. G. F. Chew and F. E. Low have given a solution [Proceedings of the Rochester Conference, 1955 (Interscience Publishers, Inc., New York, 1955)]

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Phys. Rev. 101, 453– Published 1 January, 1956
  • Received 3 August 1955

© 1956 American Physical Society

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