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Il Nuovo Cimento A (1965-1970)

, Volume 19, Issue 3, pp 395–429 | Cite as

Vertex bootstrap for the fine-structure constant

  • F. Englert
  • J. M. Frère
  • P. Nicoletopoulos
Article

Summary

The possibility of converting the Baker-Johnson-Adler eigenvalue equationF(α)=0 for the fine-structure constant into a simpler condition is discussed in the framework of the self-consistent (bootstrap) formulation of massless quantum electrodynamics. It is shown that the imposition of a strong convergence condition on the vertex bootstrap equation in the canonical (generalized Landau) gauge leads to an eigenvalue equation for α,\(\tilde Z_{1c} \left( \alpha \right) = 0\), which is consistent with the gauge covariance of the theory and impliesF(α)=0. The function\(\tilde Z_{1c} \left( \alpha \right)\) may be expanded in a power series in α through Feynman graphs.

Бутстрап вершины для постоянной тонкой структуры

Резюме

В рамках самосогласованной (бутстрап) формулировки безмассовой квантовой электродинамики обсуждается возможность преобразования уравнения Бакере-Джонсона-АдлераF(α)=0 для собственных значений постоянной тонкой структуры в более простое условие. Показывается, что наложение условия сильной сходимости на уравнение бутстрапа вершины в канонической калибровке (обобщенной калибровке Ландау) приводит к кравнению собственных значений для α,\(\tilde Z_{1c} \left( \alpha \right) = 0\), которое согласуется с калибровочной коваринтностью теории и которое имеет следствиемF(α)=0. Функция\(\tilde Z_{1c} \left( \alpha \right)\) может быть разложена в степенной ряд по α через фейнмановские диаграммы.

Riassunto

Si discute nello schema della formulazione autoconsistente (bootstrap) dell'elettrodinamica quantistica in assenza di masse la possibilità di convertire l'equazione agli autovaloriF(α)=0 di Baker-Johnson-Adler per la costante di struttura fine in una condizione più semplice. Si dimostra che l'imposizione di una forte condizione di convergenza all'equazione di bootstrap di vertice nella gauge canonica (generalizzata di Landau) conduce ad una equazione agli autovalori in α,\(\tilde Z_{1c} \left( \alpha \right) = 0\), che risulta consistente con la covarianza di gauge della teoria ed implica che siaF(α)=0. La funzione\(\tilde Z_{1c} \left( \alpha \right)\) si può sviluppare in serie di potenze di α mediante grafici di Feynman.

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Copyright information

© Società Italiana di Fisica 1974

Authors and Affiliations

  • F. Englert
    • 1
    • 2
  • J. M. Frère
    • 2
  • P. Nicoletopoulos
    • 2
    • 3
  1. 1.CENSaclay
  2. 2.Faculté des SciencesUniversité Libre de BruxellesBruxelles
  3. 3.CERNGenève

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