GGI lectures on boundary and asymptotic symmetries

TL;DR

This paper provides comprehensive lecture support on boundary and asymptotic symmetries in gravity, including derivations of BMS groups and Hamiltonian generators, aimed at advancing understanding of flat holography and gauge theories.

Contribution

It offers original, pedagogical derivations of BMS symmetries and Hamiltonian generators using Minkowski space and scalar fields, enhancing educational resources in asymptotic symmetries.

Findings

Derivation of BMS group using Minkowski space

Hamiltonian generator for scalar field diffeomorphisms

Clarification of flux-balance laws on null hypersurfaces

Abstract

Support material for lectures at the May '25 Galileo Galilei Institute school on asymptotic sym- metries 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.