Summary
In local field theories the form factors of particles can have singularities which are characteristic for the structure of these particles as composite systems. These « structure singularities » are studied with the help of examples from perturbation theory. Their mathematical properties are described for real and complex values of the mass variable, and their physical implications are discussed.
Riassunto
Nelle teorie di campo locali i fattori di forma delle particelle possono presentare singolarità caratteristiche della struttura di tali particelle come sistemi composti. Si studiano queste « singolarità di struttura » con l’ausilio di esempi presi dalla teoria delle perturbazioni. Si descrivono le loro proprietà matematiche per valori reali e complessi della variabile di massa e se ne discute il significato fisico.
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References
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The pion cloud of the nucleon must be folded into this long-range distribution; it changes the distribution, but does not affect the slope. One can easily draw corresponding Feynman diagrams, which then can be reduced, for the purpose of their analytic structure, to simpler graphs similar to that given in Fig. 1. See ref. (5),Y. Nambu:Nuovo Cimento,6, 1064 (1957) andK. Symanzik:Prog. Theor. Phys.,20, 690 (1958).
W. Zimmermann:Nuovo Cimento,10, 597 (1958);R. Haag:Phys. Rev.,112 669 (1958);K. Nishijima:Phys. Rev.,111, 995 (1958). These papers contain further references.
The exact shape of this region where singularities are allowed is not known at present. It depends upon the mass variable and the special conditions. See ref. (2,3) andR. Oehme:Proceedings of the 1958Annual International Conference on High Energy Physics at CERN, edited byB. Ferretti (CERN, Geneva 1958).
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Work supported in part by the U.S. Atomic Energy Commission.
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Oehme, R. Structure singularities of electromagnetic form factors. Nuovo Cim 13, 778–789 (1959). https://doi.org/10.1007/BF02726365
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DOI: https://doi.org/10.1007/BF02726365