Abstract

An asymptotic solution of an equation of Bethe–Salpeter type in the massive theory with λφ 4 interaction is investigated in the ladder approximation. The main problem is to work out a recipe to ground a concrete asymptotic solution of equations of Bethe–Salpeter type for amplitudes in models with 4-fermion interaction in different regions of variation of the momentum. An integral equation for the imaginary part of the forwardscattering amplitude with two-particle irreducible kernel is used. An explicit expression is found for the kernel, which consists of a simple bubble and comprises part of the kernel of the considered equation. The corresponding equation is solved in the deeply inelastic region of momenta in the form of a power-law function.

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