The Structure of the Bern-Kosower Integrand for the N-Gluon Amplitude

TL;DR

This paper refines the Bern-Kosower integrand structure for N-gluon amplitudes, ensuring permutation symmetry and revealing a recursive, gauge-invariant decomposition.

Contribution

It introduces a canonical, permutation symmetric form of the Bern-Kosower representation for one-loop N-gluon amplitudes, highlighting a recursive structure.

Findings

Achieves permutation symmetry in the integrand

Provides a natural, gauge-invariant decomposition

Reveals a simple recursive structure

Abstract

An ambiguity inherent in the partial integration procedure leading to the Bern-Kosower rules is fixed in a way which preserves the complete permutation symmetry in the scattering states. This leads to a canonical version of the Bern-Kosower representation for the one-loop N - photon/gluon amplitudes, and to a natural decomposition of those amplitudes into permutation symmetric gauge invariant partial amplitudes. This decomposition exhibits a simple recursive structure.