Summary
A compact method of expressing then-th orderS-matrix element in quantum electrodynamics has been given byCaianiello. The generalization of this formula ton-interacting fields of arbitrary character is considered here. The specific example of the quantum electrodynamics of spin-0 mesons is treated. Although only two fields are present there are several interactions because of thee 2 term in the current and because of the meson-meson renormalization term. Using these methods a new demonstration is given of the theorem that the terms in the expansion of theS-matrix that depend on the orientation of a family of space-like surfaces vanish identically.
Riassunto
Un metodo compatto per esprimere l’elemento di ordinen-simo della matriceS in elettrodinamica quantistica è stato dato daCaianiello. Qui si considera la generalizzazione di questa formula adn campi interagenti di carattere arbitrario. Viene trattato l’esempio specifico dell’elettrodinamica quantistica dei mesoni di spin 0. Per quanto siano presenti solo due campi, ci sono parecchie interazioni a causa del terminee 2 nella corrente e del termine di rinormalizzazione mesone-mesone. Usando questi metodi si dà una nuova dimostrazione del teorema secondo il quale i termini nello sviluppo della matriceS che dipendono dall’orientazione di una famiglia di superficie spazio-simili, si annullano identicamente.
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References
E. R. Caianiello:Nuovo Cimento,11, 492 (1954), referred to as I.
F. J. Dyson:Phys. Rev.,5, 486 (1949).
F. Rohrlick:Phys. Rev.,80, 666 (1950).
A. Salam:Phys. Rev.,86, 731 (1952).
P. T. Matthews:Phys. Rev.,80, 292 (1950).
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The research reported in this document has been sponsored i part by the Office Chief of Research and Development, U. S. Department of Army, through its European Office under contract no. DA-91-591-EUC-1096.
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Halpern, F.R. A compact expression forS-matrix elements in theories with several interacting fields. Nuovo Cim 16, 1085–1091 (1960). https://doi.org/10.1007/BF02860390
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DOI: https://doi.org/10.1007/BF02860390