Summary
An investigation is made of the convergence of the field-theoretic perturbation expansion of the elements of theS-matrix. For a theory characterized by a coupling linear in the boson field, it is established that if a cut-off is introduced in momentum space, then the transition amplitude for any given process over a finite-time interval, is bounded term by term by an exponential series. The extension of the method to interactions which are not linear, is, for several cases, also included. The implications of the result for theories without a cut-off is discussed from a qualitative point of view.
Riassunto
Si esamina la convergenza dello sviluppo degli elementi della matriceS secondo la teoria della perturbazione del campo. Per una teoria caratterizzata da un accoppiamento lineare nel campo bosonico si constata che introducendo un taglio nello spazio dei momenti l’ampiezza di transizione per ogni processo in un intervallo di tempo finito è limitata termine a termine da una serie esponenziale. Si espone anche per diversi casi l’estensione del metodo ad interazioni non lineari. Si discutono da un punto di vista qualitativo le conseguenze che dal risultato emergono per le teorie prive di taglio.
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The greater part of this appendix was prepared byM. M. Schiffer.
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Supported in part by the United States Air Force through the Office of Scientific Research, Air Research and Development Command.
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Yennie, D.R., Gartenhaus, S. Convergence of theS-matrix. Nuovo Cim 9, 59–76 (1958). https://doi.org/10.1007/BF02892253
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DOI: https://doi.org/10.1007/BF02892253