On the Open String Ending on D-brane

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We obtain background independent solutions for an open string ending on D-brane, in variable external fields. Explicit solution of the boundary conditions is given for background metric and NS-NS two-form gauge field, depending on the coordinates of the transverse to the Dp-brane directions. Extension of the constraint algebra is proposed and discussed from both Hamiltonian and Lagrangian approach viewpoint.
LaTeX, 14 pages, no figures; V2: cosmetic changes, invited paper for the Volume "Frontiers in Field Thory", O. Kovras, ed. (Nova Science Publishers, NY)

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