Open String Field Theory on Noncommutative Space

We study Witten's open string field theory in the presence of a constant B field. We construct the string field theory in the operator formalism and find that, compared to the ordinary theory with no B field, the vertices in the resulting theory has an additional factor. This factor makes the zero modes of strings noncommutative. This is in agreement with the results in the first-quantized formulation. We also discuss the background independence of the purely cubic action derived from the above mentioned string field theory and then make a redefinition of string fields to remove the additional factor from the vertex. Furthermore, we briefly discuss the supersymmetric extension of our string field theory.