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Algebraic Equations for Bethe‐Salpeter and Coulomb Green's Functions

### Abstract

The equation for the Bethe‐Salpeter Green's function in the case of two scalar quarksinteracting via the exchange of a scalar particle of zero mass is transformed to an algebraic equation with the help of the dynamical group *SO*(5, 2). From this equation a one‐parameter integral representation of the Green's function is obtained in the case of maximal binding, and from this representation the Green's function is calculated in terms of a hypergeometric function. The equation for the *f*‐dimensional nonrelativistic Coulomb Green's function is also transformed to an algebraic equation.

© 1972 The American Institute of Physics

Received 07 February 1972
Published online 31 October 2003