Numerical solution of the spinor Bethe--Salpeter equation and the Goldstein problem

Journal Article · Tue Aug 01 04:00:00 EDT 1978 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(78)90204-X· OSTI ID:6877334

Suttorp, L G

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.

• Research Organization: Institute of Theoretical Physics, University of Amsterdam, Amsterdam, The Netherlands
• OSTI ID: 6877334
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 113:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BETHE-SALPETER EQUATION
BINDING ENERGY
BOUND STATE
COUPLING CONSTANTS
ENERGY
EQUATIONS
FERMIONS
FIELD THEORIES
NUMERICAL SOLUTION
PARITY
PARTICLE PROPERTIES
QUANTUM FIELD THEORY