Proof of perturbative gauge invariance for tree diagrams to all orders

TL;DR

This paper proves that classical BRS-invariance ensures perturbative gauge invariance for tree diagrams at all orders, including applications to gravity's Einstein-Hilbert Lagrangian.

Contribution

It establishes a general proof linking classical BRS-invariance to perturbative gauge invariance for all orders in tree diagrams, applicable to gravity.

Findings

Classical BRS-invariance implies perturbative gauge invariance for tree diagrams.

The proof applies to the Einstein-Hilbert Lagrangian of gravity.

Perturbative gauge invariance holds to all orders for tree diagrams.

Abstract

It is proved that classical BRS-invariance of the Lagrangian implies perturbative gauge invariance for tree diagrams to all orders. The proof applies in particular to the Einstein Hilbert Largrangian of gravity.