NON-ABELIAN GAUGE FIELD-DYNAMICS ON MATRIX D-BRANES

We construct a calculational scheme for handling the matrix ordering p roblems connected with the appearance of D-brane positions taking valu es in the same Lie algebra as the non-abelian gauge field living on th e D-brane. The formalism is based on the use of a one-dimensional auxi liary field living on the boundary of the string world-sheet and takin g 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 positio n is derived in lowest order of the alpha' expansion. (C) 1997 Elsevie r Science B.V.