On the Lagrangian and Hamiltonian formulation of a scalar free field theory at null infinity

In the framework of asymptotically flat spacetimes, we discuss the notion of a covariant scalar free field at null infinity. We construct the associated equations of motion exploiting either the theory of induced representations or the white noise analysis. Eventually, we prove that these equations can also be derived as the minimum of a suitable Lagrangian and that a real scalar field theory at null infinity admits a Hamiltonian formulation.