  Noncommutativity in an open bosonic string moving in the presence of a
background Neveu-Schwarz two-form field $B_{\mu \nu}$ is investigated in a
conformal field theory approach, leading to noncommutativity at the boundaries.
In contrast to several discussions, in which boundary conditions are taken as
Dirac constraints, we first obtain the mode algebra by using the newly proposed
normal ordering, which satisfies both equations of motion and boundary
conditions. Using these the commutator among the string coordinates is
obtained. Interestingly, this new normal ordering yields the same algebra
between the modes as the one satisfying only the equations of motion. In this
approach, we find that noncommutativity originates more transparently and our
results match with the existing results in the literature.
