Nonlinear couplings and tree amplitudes in gauge theories

TL;DR

This paper investigates how nonlinear gauge particle interactions relate to gauge invariance of tree amplitudes, demonstrating that these constraints uniquely determine Yang-Mills theory but not gravity.

Contribution

It establishes a link between nonlinear vertices and gauge invariance, uniquely fixing the structure of Yang-Mills theory under certain assumptions.

Findings

Nonlinear vertices are constrained by gauge invariance.

Yang-Mills theory structure is uniquely determined.

Gravity gauge theory is not uniquely fixed by these constraints.

Abstract

Following a remark advanced by Feynman,we study the connection between the form of the nonlinear vertices involving gauge particles and the Abelian gauge invariance of physical tree amplitudes. We show that this requirement, together with some natural assumptions, fixes uniquely the structure of the Yang-Mills theory. However, the constraints imposed by the above property are not sufficient to single out the gauge theory of gravitation.