Summary
In this paper, we develop the theory of the four-point function for a two-component field, satisfying a nonlinear equation which is a simplified form of the basic equation of Heisenberg’s theory of elementary particles, in its formulation by means of Weyl isospinors due to Dürr. The underlying Pauli algebra enables us to achieve a remarkable compactness of the final results; moreover, their physical interpretation turns out to be somewhat clearer (as compared with the original scheme, based on the usual formulation of Heisenberg’s theory). In particular, the connection with the two-point function and the « regularization conditions » (following from the differential equation) are investigated in some detail.
Riassunto
In questo lavoro, si sviluppa la teoria della funzione a quattro punti per un campo a due componenti, soddisfacente ad una equazione non lineare che è una forma semplificata dell’equazione fondamentale della teoria di Heisenberg delle particelle elementari, nella sua formulazione in termini di isospinori di Weyl dovuta a Dürr. L’uso dell’algebra di Pauli permette di dare una notevole compattezza ai risultati finali inoltre, il loro significato fisico risulta alquanto più chiaro (rispetto allo schema originale, basato sulla usuale formulazione della teoria di Heisenberg. In particolare, si studiano in dettaglio la connessione con la funzione a due punti e le « condizioni di regolarizzazione » (conseguenti dall’equazione differenziale).
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References
E. Montaldi:Nucl. Phys.,23, 439 (1961), hereafter referred to as I.
H. P. Dürr, W. Heisenberg, H. Mitter, S. Schlieder andK. Yamazaki:Zeits. f. Naturfor., A14, 441 (1959).
H. Mitter: private communication. The author is indebted to Dr.Mitter for having brought his attention on this point.
H. P. Dürr:Zeits. f. Naturfor, A16, 327 (1961).
This section is due substantially toH. Mitter, to whom the author is indebted for a correspondence on the subject.
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Montaldi, E. The four-point function for a nonlinear two-component field, and its connections with heisenberg’s theory of elementary particles. Nuovo Cim 25, 1167–1182 (1962). https://doi.org/10.1007/BF02733737
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DOI: https://doi.org/10.1007/BF02733737