Abstract
The finite energy sum rules (FESR) are a tool for investigating the structure of scattering amplitudes. Together with this technique there goes a certain philosophy. We try to explain both in this lecture. We do not present a complete survey of the subject and, therefore, many important contributions are omitted. We prefer to discuss several cases that can serve as a good example of the technique and a foundation for the philosophy.
Work sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under AFOSR grant number E00AR-68-0010, through the European Office of Aerospace Research.
Lecture given at the VIII. Internationale Universitätswochen für Kernphysik, Schladming, February 24–March 8, 1969.
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Footnotes and References
D. Horn and C. Schmid, CALT-68-127 (1367), unpublished. A general analysis of theory and applications which we follow quite closely here is given by R. Dolen, D. Horn and C. Schmid, Phys. Rev. 166, 1768 (1968).
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Note that an odd (even)amplitude has an odd (even) real part and an even (odd) imaginary part. Therefore the right-signature FESR, that can be derived by integrations from-N to N are even (odd) respectively. The wrong signature FESR lead to Schwarz superconvergence relations; J. H. Schwarz, Phys. Rev. 159, 1269 (1967).
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D. Horn and C. Schmid, ref. 1. These papers were based on a method introduced and applied by K. Igi, Phys. Rev. Lett. 9, 76 (1962) to an investigation of the Pomeranchukon.
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Horn, D. (1969). Finite Energy Sum Rules — Use and Interpretation. In: Urban, P. (eds) Particle Physics. Acta Physica Austriaca, vol 6/1969. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7638-2_5
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