GGI lectures on boundary and asymptotic symmetries

Abstract

Support material for lectures at the May '25 Galileo Galilei Institute school on asymptotic symmetries and flat holography. Contains an introduction to Noether theorem for gauge theories and gravity, covariant phase space formalism, boundary and asymptotic symmetries, flux-balance laws on null hypersurfaces, future null infinity in Bondi-Sachs coordinates and with Penrose's conformal compactification, BMS symmetries and their charges and fluxes. Includes an original and pedagogical derivation of the BMS group using only Minkowski, and an original derivation of an integral Hamiltonian generator for diffeomorphisms of a scalar field on a null hypersurface.

v2: largely rewritten for better clarity with extended discussions and examples. Various numerical factors fixed. Expanded bibliography. v3: some corrections and various text improvements. Contains additional typos corrected and references updated with respect to the published version. 77 pages, 4 figure