On the nullification of threshold amplitudes

TL;DR

This paper investigates the nullification of threshold amplitudes in quantum field theory, deriving Ward identities to prove the vanishing of tree-graph threshold amplitudes within the conventional framework.

Contribution

It provides a rigorous proof of threshold amplitude nullification using Ward identities, enhancing understanding of amplitude behavior in quantum field theory.

Findings

Ward identities are derived for the reduced theory.

Tree-graph threshold amplitudes are shown to vanish.

The proof is established on both path-integral and diagrammatic levels.

Abstract

The nullification of threshold amplitudes is considered within the conventional framework of quantum field theory. The relevant Ward identities for the reduced theory are derived both on path-integral and diagrammatic levels. They are then used to prove the vanishing of tree-graph threshold amplitudes.