Summary
A covariant method of approximating the nucleon Green’s functionS′ F is described, in terms of the solution of a connected sequence of linear integral equations. Explicit expressions for the matrix elements for processes involving only one real nucleon are derived by formal functional differentiation ofS′ F with respect to external boson fields. The solution is renormalized, in the sense that its power series expansion in the coupling constantg is the same that obtained by enumerating Feynman diagrams and renormalizing term by term. Closed loops are neglected, though virtual nucleon pairs not corresponding to closed loops are included.
Riassunto
In termini della soluzione di una sequenza connessa di equazioni integrali lineari si descrive un metodo covariante per l’approssimazione della funzione nucleonica di GreenS′ F . Per differenziazione funzionale formale diS′ F rispetto al campo bosonico esterno si ottengono espressioni esplicite per gli elementi di matrice di processi che coinvolgono un solo nucleone reale. Si rinormalizza la soluzione nel senso che il suo sviluppo in serie di potenze della costante d’accoppiamentog è uguale a quello ottenuto enumerando i diagrammi di Feynman e rinormalizzando termine a termine. Si trascurano le anse chiuse, pur includendo coppie virtuali di nucleoni non corrispondenti ad anse chiuse.
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Much of this work was performed at Brookhaven National Laboratory, Upton, New York, under the auspices of the U.S. Atomic Energy Commission.
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Mills, R.L. Integral equations for meson field theory. Nuovo Cim 5, 30–44 (1957). https://doi.org/10.1007/BF02812815
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DOI: https://doi.org/10.1007/BF02812815