Witten's open string field theory in constant B-field background

In this paper we consider Witten's bosonic open string field theory in thepresence of a constant background of the second-rank antisymmetric tensor field$B_{ij}$. We extend the operator formulation of Gross and Jevicki in thissituation and construct the overlap vertices explicitly. As a result we find anoncommutative structure of the Moyal type only in the zero-mode sector, whichis consistent with the result of the correlation functions among vertexoperators in the world sheet formulation. Furthermore we find out a certainunitary transformation of the string field which absorbs the Moyal typenoncommutative structure. It can be regarded as a microscopic origin of thetransformation between the gauge fields in commutative and noncommutative gaugetheories discussed by Seiberg and Witten.Comment: 35 pages, LaTeX, no figures, Arguments about string coupling constants are modified. final version to be published in JHE