Programme Speaker: Michael Dütsch Title: BRS-symmetry and perturbative gauge invariance in classical gravity Abstract: Given a free BRS-invariant gauge field theory, perturbative gauge invariance (PGI) (which is a condition that is related to BRS-invariance) can be used to derive the possible interactions. For a massless symmetric tensor field $h^{\mu\nu}$ and a polynomial ansatz for the interaction ${\cal L}=\sum_{n=1}^\infty\kappa^n\,{\cal L}^{(n)}$ (where $\kappa$ is the coupling constant), it has been worked out that the most general solutions for ${\cal L}^{(1)}$ and ${\cal L}^{(2)}$ agree with the corresponding terms of the Einstein-Hilbert Lagrangian (where $\sqrt{-g(x)}\, g^{\mu\nu}(x)=\eta^{\mu\nu}+\kappa\,h^{\mu\nu}(x)\ ,\>\eta^{\mu\nu}=$ Minkowski metric) up to physically irrelevant terms (Scharf, Schorn, Wellmann). But continuing this procedure to higher orders the amount of computational work increases strongly and, due to the non-renormalizability of spin-2 gauge fields, one never comes to an end. Our main result is that the Einstein-Hilbert Lagrangian, completed by a gauge fixing and a Faddeev-Popov ghost term, yields a solution of PGI to all orders in $\kappa$. This result is restricted to classical gravity or equivalently to the tree diagrams of perturbative QFT. We generally prove that classical BRS-invariance of the Lagrangian (i.e. $s{\cal L}=-\partial_\mu I^\mu$ for some $I^\mu$) implies perturbative gauge invariance for tree diagrams to all orders.