arXiv:hep-th/0502071v2 4 Apr 2005 Proof of perturbative gauge invariance for tree diagrams to all orders Michael D¨ utsch Institut f¨ ur Theoretische Physik Universit¨atZ¨ urich CH-8057 Z¨ urich, Switzerland duetsch@physik.unizh.ch Abstract It is proved that classical BRS-invariance of the Lagrangian im- plies perturbative gauge invariance for tree diagrams to all orders. The proof applies in particular to the Einstein Hilbert Largrangian of gravity. PACS. 11.15.Bt Gauge field theories: General properties of pertur- bation theory Contents 1 Introduction 2 2 From classical current conservation to perturbative gauge invariance for tree diagr 3 From BRS-invariance of the Lagrangian to local conservation of the classical BRS- 4 Models 21 4.1 Massless Yang-Mills theories ................... 21 4.2 Massive spin-1 fields ....................... 23 4.3 Massless spin-2 gauge fields ................... 26 1