  The formal extension of the T-duality rules for open strings from Abelian to
non-Abelian gauge field background leads in a well known manner to the notion
of matrix valued D-brane position. The application of this concept to the
non-Abelian gauge field RG $\beta $-function of the corresponding $\sigma
$-model yields a mass term in the gauge field dynamics on the matrix D-brane.
The direct calculation in a corresponding D-brane model does $not$ yield such a
mass term, if the Dirichlet boundary condition is implemented as a constraint
on the integrand in the defining functional integral. However, the mass term
arises in the direct calculation for a D-brane model with dynamically realized
boundary condition.
