  Boundary conditions play a non trivial role in string theory. For instance
the rich structure of D-branes is generated by choosing appropriate
combinations of Dirichlet and Neumann boundary conditions. Furthermore, when an
antisymmetric background is present at the string end-points (corresponding to
mixed boundary conditions) space time becomes non-commutative there.
  We show here how to build up normal ordered products for bosonic string
position operators that satisfy both equations of motion and open string
boundary conditions at quantum level. We also calculate the equal time
commutator of these normal ordered products in the presence of antisymmetric
tensor background.
