  Generally, open string boundary conditions play a nontrivial role in string
theory. For example, in the presence of an antisymmetric tensor background
field, they will lead the spacetime coordinates noncommutative. In this paper,
we mainly discuss how to build up a generalized Dirichlet normal ordered
product of open bosonic string embedding operators that satisfies both the
equations of motion and the generalized Dirichlet boundary conditions at the
quantum level in the presence of an antisymmetric background field, as the
generalized Neumann case has already been discussed in the literature. Further,
we also give a brief check of the consistency of the theory under the newly
introduced normal ordering.
