Summary
The unrenormalized Schwinger-Dyson equation for the vertex function of quantum electrodynamics is discussed in the first approximation of the semi-perturbative scheme of Johnson, Baker and Willey. It is found that the equation does not possess a unique bounded solution. The most general solution consistent with Ward's identity is obtained, and this yields an infinite value for the charge renormalization constant, Z −13 .
Riassunto
Si discute l'equazione di Schwinger-Dyson non rinormalizzata per la funzione di vertice dell'elettrodinamica quantica, nella prima approssimazione dello schema semiperturbativo di Johnson, Baker e Willey. Risulta che l'equazione non possiede un'unica soluzione limitata. Si ottiene la soluzione più generale coerente con l'identità di Ward, e ciò fornisce un valore infinito per la costante di rinormalizzazione della carica, Z −13 .
Резюме
Обсуждается неперенормированное уравнение Швинтера-Дайсона для вершинной функции квантовой электродинамики в первом приближении полупертурбационной схемы Джонсона, Бакера и Виллея. Обнаружено, что уравнение не имеет единственного ограниченного решения. Получается наиболее общее решение, согласующееся с тождеством Уорда, которое даёт бесконечное значение для перенормировочной константы заряда, Z −13 .
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Literatur
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To obtain this result we note that the vertex equations for the combinations (m−2l 3) and (g 2−2f 2) which appear in the expression forZ 3 have no logarithmic terms. Hence, as was the case with eq. (19), their asymptotic dependences are correctly determined by perturbation theory. On substitutingf=1 into the right-hand sides of the vertex equations, and including electron mass terms in the manner outlined in footnote (11), the above result is obtained. It may, of course, be much more easily derived: for example in the manner followed (6)J. L. Rosner:Phys. Rev. Lett.,17, 1190 (1960) but taking account of the different vertex equation used there.
R. Jost andJ. M. Luttinger:Helv. Phys. Acta,23, 201 (1950).
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Traduzione a cura della Redazione.
Перевебено ребакцией.
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Yock, P.C.M. A semi-perturbative analysis of charge renormalization. Nuovo Cimento A (1965-1970) 55, 217–232 (1968). https://doi.org/10.1007/BF02759224
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DOI: https://doi.org/10.1007/BF02759224