Asymptotic structure of a massless scalar field and its dual two-form field at spatial infinity

Understand

Relativistic field theories with a power law decay in $r^{-k}$ at spatial infinity generically possess an infinite number of conserved quantities because of Lorentz invariance.

• Most of these are not related in any obvious way to symmetry transformations of which they would be the Noether charges.
• We discuss the issue in the case of a massless scalar field.
• By going to the dual formulation in terms of a $2$-form (as was done recently in a null infinity analysis), we relate some of the scalar charges to symmetry transformations acting on the $2$-form and on surface degrees of freedom that must be added at spatial infinity.