On the validity of various approximations for the Bethe-Salpeter equation and their WKB-quantization

The validity of the instantaneous approximation for the Bethe-Salpeter equation is questioned within the framework of the simple scalar-scalar model of Cutkovski. Detailed numerous results for various approximations are compared to the exact ones. WKB-quantization is applied to these relativistic approximations. An unexpected question arises: is the currently used Bethe-Salpeter equation (i.e. the ladder approximation) well suited to describe two interacting relativistic particles