Non-abelian gauge field dynamics on matrix D-branes

We construct a calculational scheme for handling the matrix ordering problems connected with the appearance of D-brane positions taking values in the same Lie algebra as the non-abelian gauge field living on the D-brane. The formalism is based on the use of a one-dimensional auxiliary field living on the boundary of the string world-sheet and taking care of the order of the matrix-valued fields. The resulting system of equations of motion for both the gauge held and the D-brane position is derived in lowest order of the alpha' expansion. (C) 1997 Elsevier Science B.V.