Functional reduction of the S matrix in the canonical formalism

Abstract

The Low equation is derived in a functional approach to the reduction of the S matrix in the canonical formalism. This establishes the vacuum expectation value of the scattering matrix as the generating functional of non-forward Green functions, without reference to external currents. The method provides an alternate derivation of non-perturbative results of field theory, such as the Low equation, and considerably simplifies their derivation as well as that of the rules of perturbation theory, the LSZ reduction formula, the Dyson-Schwinger equations and crossing symmetry. The approach is employed to further develop the Low equation via reduction of the fermionic sector to obtain a reduced Dyson-Schwinger equation for boson-fermion scattering.