Seminar of Theory of Relativity and Gravitation

The quantization of General Relativity (GR) is an old and challenging problemthat is in many ways still awaiting a satisfactory solution. GR is a particularly complicated field theory in several respects: non-linearity, gauge invariance, dynamical causal structure, renormalization, singularities, infrared effects. Our understanding of these problems has evolved over the past centuries together with our understanding of quantum field theory (QFT) in general. Today, the state of the art in QFT knows how to address each of these challenges, as they occur in isolation in other field theories. It is still a challenge to combine the relevant methods and apply them to GR, but at the very least the problem of the quantization of GR can be formulated as a well defined mathematical question. I will sketch this formulation paying attention to the following methods: covariant Poisson structure, BV-BRST treatment of gauge theories, deformation quantization, Epstein-Glaser renormalization.