Functional reduction of the S matrix in the canonical formalism

TL;DR

This paper introduces a functional approach to reduce the S matrix in the canonical formalism, simplifying the derivation of key non-perturbative results and extending the Low equation to fermionic sectors.

Contribution

It provides an alternative derivation of the Low equation and related field theory results using a functional method that simplifies the process and extends to fermion-boson interactions.

Findings

Derived the Low equation via a functional approach

Simplified derivation of perturbation theory rules and crossing symmetry

Extended the Low equation to include fermionic sectors

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.