Field theoretical approach to gravitational waves

The aim of these notes is to give an accessible and self-contained introduction to the theory of gravitational waves as the theory of a relativistic symmetric tensor field in a Minkowski background spacetime. This is the approach of a particle physicist: the graviton is identified with a particular irreducible representation of the Poincar\'e group, corresponding to vanishing mass and spin two. It is shown how to construct an action functional giving the linear dynamics of gravitons, and how General Relativity can be obtained from it. The Hamiltonian formulation of the linear theory is examined in detail. We study the emission of gravitational waves and apply the results to the simplest case of a binary Newtonian system.