Open-string endpoint momentum flux
= Open-string endpoint momentum flux
{title2=$J_m=eT^2X'_m+uP_m$}
For the <Nambu-Goto phase-space action>, $\dot P_m=\partial_\sigma J_m$ with $J_m=eT^2X'_m+uP_m$. Thus $\dot{\mathcal P}_m=J_m(\pi)-J_m(0)$. Free endpoint variations force $J_m=0$ individually. A <Dirichlet boundary condition> allows an external support or <D-brane> to absorb momentum in the fixed direction.