Summary
The forward scattering amplitudeM(ω) (real partD(ω), imaginary partA(ω)) in pion nucleon scattering is discussed when the acausal spread of the current commutator over the space-like interval is very small. If the acausal smearing is so small as to justify the treating of its effect as a perturbation, the errors of the dispersion relations are proved to be energy independent in the first order approximation. Hence, there would be no guarantee of affecting micro-causality even if the dispersion relations written, as they are, in a form of subtractionD(ω) —D(μ) could be in agreement with the experiment.
Riassunto
Si discute l’ampiezza di scattering in avantiM(ω) (parte realeD(ω), parte immaginariaA(ω)) dello scattering pione nucleone, quando la diffusione acausale del commutatore di corrente nell’intervallo spaziale è piccolissima. Se la diffusione acausale è tanto piccola da poter trattare il suo effetto come una perturbazione, gli errori delle relazioni di dispersione risultano indipendenti dall’energia nell’approssimazione del primo ordine. Non si avrebbe quindi alcuna garanzia dell’influenza della microcausalità anche se le relazioni di dispersione, scritte come sono in forma di differenza,D(ω) −D(μ), potessero accordarsi coi risultati sperimentali.
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Ito, D., Minami, S. & Tanaka, H. A note on an acausality test (II). Nuovo Cim 9, 461–469 (1958). https://doi.org/10.1007/BF02725102
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DOI: https://doi.org/10.1007/BF02725102