Summary
The backscattering probability amplitude between two massive fermions whose interactions are described by the two-dimensional Federbush model is calculated to second order in renormalized perturbation theory. The calculation yields a nonvanishing amplitude which is in direct conflict with the prediction of a trivial scattering matrix derived from an exact solution of this model studied by Federbush and Wightman.
Riassunto
Si calcola con la precisione del secondo ordine nella teoria perturbativa rinormalizzata l’ampiezza di probabilità dello scattering all’indietro fra due fermioni dotati di massa di cui si descrivono le interazioni con il modello bidimensionale di Federbush. Dal calcolo risulta un’ampiezza che non tende a zero, il che è in diretto contrasto con la previsione di una matrice di scattering ovvia dedotta da una soluzione esatta di questo modello studiata da Federbush e Wightman.
Реэюме
Во втором порядке перенормированной теории воэмушений вычи-сляется амплитуда рассеяния наэад для двух массивных фермионов, вэаимодействие которых описывается с помошью двухмерной модели Федербуща. Вычисление дает ненулевую амплитуду, которая непосредственно противоречит предскаэанию тривиальной матрицы рассеяния, выведенной иэ точного рещения для зтой модели, исследованной Федербущем и Вайтманом.
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References
P. Federbush:Phys. Rev.,121, 1247 (1961).
A. S. Wightman: inCargèse Lectures in Theoretical Physics, edited byM. Lévy (New York, N. Y., 1964), p. 171.
K. Hepp:Comm. Math. Phys.,2, 301 (1966), eqs. (1.7)-(1.9).
N. Bogoliubov andD. Shirkov:Introduction to the Theory of Quantized Fields (New York, N. Y., 1959).
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Tapper, M.L. A possible conflict between renormalized perturbation theory and an exact solution of the two-dimensional federbush model describing the pseudoscalar interaction of two massive fermions. Nuov Cim A 25, 165–172 (1975). https://doi.org/10.1007/BF02735617
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DOI: https://doi.org/10.1007/BF02735617