A points-splitting and dimensional renormalization: P. S. Collecott, Max-Planck-Institut für Physik und Astrophysik, Postfach 40 12 12, D-8000 München 40, Federal Republic of Germany

• Publisher: Elsevier Science
• Year: 1978
• Tongue: English
• Weight: 80 KB
• Volume: 113
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(78)90258-0

✦ Synopsis

The spinor Bethe-Salpeter equation describing bound states of a fermion-antifermion pair with massless-boson exchange reduces to a single (uncoupled) partial differential equation for special combinations of the fermion-boson couplings. For spinless bound states with positive or negative parity this equation is a generalization to nonvanishing bound-state masses of the equations studied by Kummer and Goldstein, respectively. In the tight-binding limit the Kummer equation has a discrete spectrum, in contrast to the Goldstein equation, while for loose binding only the generalized Goldstein equation has a nonrelativistic limit. For intermediate binding energies the equations are solved numerically. The generalized Kummer equation is shown to possess a discrete spectrum of coupling constants for all bound-state masses. For the generalized Goldstein equation a discrete spectrum of coupling constants is found only if the binding energy is smaller than a critical value.

A Points-Splitting and Dimensional Renormalization.