Ward Identity Implies Recursion Relation at Tree and Loop Level

TL;DR

This paper demonstrates how Ward identities lead to recursion relations for off-shell amplitudes in pure Yang-Mills theory at tree and one-loop levels, simplifying calculations and providing explicit examples.

Contribution

It introduces a novel approach using Ward identities to derive recursion relations for off-shell amplitudes at both tree and loop levels in Yang-Mills theory.

Findings

Ward identities are proven at tree and one-loop levels.

Recursion relations for off-shell amplitudes are derived.

Explicit calculations for three and four point one-loop amplitudes are provided.

Abstract

In this article, we use Ward identity to calculate tree and one loop level off shell amplitudes in pure Yang-Mills theory with a pair of external lines complexified. We explicitly prove Ward identity at tree and one loop level using Feynman rules, and then give recursion relations for the off shell amplitudes. We find that the cancellation details in the proof of Ward identity simplifies our derivation of the recursion relations. Then we calculate three and four point one loop off shell amplitudes as examples of our method.