Crossing-symmetric two-particle reduction of four-point vertex.

Abstract

We develop a nonperturbative reduction scheme for the four-point vertex [ital T] of a generic field theory with interactions among bosons, fermions, and antifermions. We exhibit integral equations which express, in a manifestly crossing-symmetric way, the full vertex in terms of its two-particle irreducible part, together with the dressed three-point vertices and two-point propagators. This scheme generalizes the usual summation of ladder or bubble diagrams, thus providing for the consistent summation of a larger subset of all diagrams.