Summary
By inspection of the relation between one-particle irreducible functions and Bethe-Salpeter kernels and making use of Weinberg's theorem the running coupling constant for a given bound state is shown to have the usual form in the short-distance region of an asymptotically free theory. This is done explicitly for a two-body bound state in the absence ofs-channel contributions which could induce difficulties. Two different choices for the boundary condition on the running coupling are pointed out, the more unconventional one is found preferable for several reasons. This difference would manifest itself unambiguously in strongly relativistic systems.
Riassunto
Esaminando la relazione tra funzioni irriducibili ad una particella e nuclei di Bethe-Salpeter e facendo uso del teorema di Weinberg si mostra che la costante di accoppiamento corrente per un dato stato legato ha la consueta forma nella regione a breve distanza di una teoria asintoticamente libera. Ciò è fatto esplicitamente per uno stato legato a due corpi in mancanza di contributi del canales che potrebbero creare difficoltà. S'illustrano due scelte diverse per la condizione al contorno dell'accoppiamento corrente, la meno convenzionale è preferibile per alcune ragioni. Questa differenza si manifesterebbe in modo non ambiguo in sistemi fortemente relativistici.
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Address after October 1, 1985: Instituut voor Theoretische Fysica, Rijksuniversiteit, Princetonplein 5, P.O. Box 80 006, NL-3508 TA Utrecht, The Netherlands.
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Kopper, C. On the running coupling constant in relativistic bound-state problems. Nuov Cim A 93, 99–112 (1986). https://doi.org/10.1007/BF02819984
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DOI: https://doi.org/10.1007/BF02819984