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Different experimental spectra relevant to inelastic protonproton interactions, at incident energies between 1 and 10 GeV, are compared with the predictions of the one-pion-exchange (OPE) model, by taking into account the production of one and two pions. This analysis gives a further confirmation of the validity of the OPE model below 3 GeV; with increasing energy, it is found that the model deteriorates rapidly, and that other effects have to be taken into account. However, the behaviour of the spectra at high energy seems to depend critically on the isospin of the exchanged system, and may be difficult to describe in terms of the pictures currently used for high-energy inelastic interactions.

The matrix element for the process of single pion production in nucleon-nucleon collisions is constructed under the hypothesis of a dominant contribution from the one-pion exchange term. The effects of the virtuality of the π-meson are fully taken into account. It is found that the finite size of the nucleon cannot be neglected. The method used allows the determination of the «pionic form factor» of the nucleon. It is shown that, by the choice of a form factor similar to the e.m. ones, a satisfactory agreement with the experiment is obtained for incident energies of (1÷3) GeV. For higher energies, the connection with a possible «Regge pole behaviour» for such reactions is briefly discussed.

A subtractionprocedure to eliminate ghosts from propagators recently proposed by Redmound is examined from the standpoint of axiomatic field theory. This procedure is bound to he equivalent to the introduction of a special vertex function which in principle can he chosen among functions having the analyticity properties prescribed by the axioms. This situation is shown to exist both in the case of boson and fermion fields. In the above discussion Lehmann integral representation of propagators is taken as an axiom by itself. The modifications brought into the discussion of ghost problems by a. subtracted Lehmann dispersion formula are then examined. Of some interest are the consequences on the high frequency behaviour of form factors. Un procedimento di sottrazione proposto recentemente da Redmond per eliminare i « ghosts » dai propagatori viens esaminato dal punto di vista della teoria assiomatica dei campi. Si trova che questo procedimento è equivalente all’introduzione di una speciale funzione vertice che in linea di principio puft essere scelta tra le funzioni che hanno le proprietà di analiticità prescritte dagli assiomi. Si mostra che tale situazione esiste sia nel caso di un campo bosonieo che nel caso di un campo fermionico. Nella discussione precedente la rappresentazione integrale di Lehmann per i propagatori è assunta essa stessa corne un assioma. Sono poi esaminate le modificazioni introdotte nella discussione del problema dei « ghosts » da una formula dispersiva alla Lehmann sottratta. Sono di un certo interesse le conseguenze sul comportamento dei fattori di forma per alte frequenze.

The problem of pion-nucleon scattering when one of the pions is virtual is discussed. By assuming that one-dimensional dispersion relations in the energy variable can be written for suitably defined invariant amplitudes, and that also in the off-shell case the dispersive integrals are dominated by the,T = J= 3/2 amplitude, an Omnès-type integral equation is deduced for this amplitude. The rigorous solution of this equation is discussed and reduced to an approximate simpler form which is more suitable for numerical calculations. This form is particularly simple for squared four-momenta of the virtual pion less than ∼ 5 squared pion masses. Si discute il problema dello scattering pione-nucleone quando uno dei pioni è virtuale. Assumendo che si possano scrivere relazioni di dispersione unidimensionali nella variabile energia per ampiezze invarianti opportunamente definite, e che anche nel caso ≪ off shell ≫ gli integrali dispersivi siano dominati dall’ampiezzaT=J= 3/2, si deduce per tale ampiezza un’equazione integrale del tipo discusso da Omnès. La soluzione esatta di tale equazione è discussa e ricondotta ad una forma approssimata più semplice e più conveniente per calcoli numerici. Tale forma è particolarmente semplice per valori del quadrato del quadri-impulso del pione virtuale minori di ∼ 5 masse pioniche quadrate.

The probability of the process π → e + v + γ is calculated by means of a cut-off procedure. It is shown that for ST coupling the branching ratio (π → e + v + γ)/(π → μ + v) is practically independent of the cut-off parameter.

The process p+p→Λ0+K++p is investigated by means of two simple models in which only the contribution of poles due to the exchange of an intermediate π0-meson or K+-meson respectively is taken into account. The total cross section is then calculated in terms of the total cross-sections for simpler processes. Numerical values are given for an energy of 3 GeV of the incident proton in the l.s.

In view of future experiments with high intensity K-meson beams the branching ratios for K±→π±+e++e−and K10→eγ are evaluated.

It is shown that the causal propagation function of a Dirac field can be split in two functions which satisfy a system of two integral equations similar to the couple of Low equations for the symmetrical charged fixed-source meson theory, in the one-meson approximation. These equations are solved and discussed. Si dimostra che la funzione causale di propagazione di un campo fermionico può essere espressa mediante due funzioni che soddisfano un sistema di due equazioni integrali, simile alla coppia di equazioni di Low per la teoria mesonica di sorgente fissa per mesoni carichi, nell’approssimazione di un solo mesone. Queste equazioni sono risolte e discusse.