Target-space Noether charges of a string
= Target-space Noether charges of a string
{title2=$\mathcal P_m=\int P_m\,d\sigma,\quad\mathcal J_{mn}=\int(X_mP_n-X_nP_m)\,d\sigma$}
Translations and <Lorentz transformations> give <Noether charges> $\mathcal P_m=\int P_m\,d\sigma$ and $\mathcal J_{mn}=\int(X_mP_n-X_nP_m)\,d\sigma$. Their time derivatives are boundary fluxes, which vanish for a <closed string> or a free-ended <open string>.