Target-space Noether charges of a string (${\mathcal{P}}_m=\int P_{m}d\sigma ,{\mathcal{J}}_{mn}=\int (X_m{P}_n-X_n{P}_m)d\sigma$)

Translations and Lorentz transformations give Noether charges ${\mathcal{P}}_m=\int P_{m}d\sigma$ and ${\mathcal{J}}_{mn}=\int (X_m{P}_n-X_n{P}_m)d\sigma$. Their time derivatives are boundary fluxes, which vanish for a closed string or a free-ended open string.