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We construct a covariant open bosonic string field theory on multipleD-branes, which reduces to a non-Abelian group Yang-Mills gauge theory in thezero-slope limit. Making use of the first quantized open bosonic string in theproper time gauge, we convert the string amplitudes given by the Polyakov pathintegrals on string world sheets into those of the second quantized theory. Theworld sheet diagrams generated by the constructed open string field theory areplanar in contrast to those of the Witten's cubic string field theory. However,the constructed string field theory is yet equivalent to the Witten's cubicstring field theory. Having obtained planar diagrams, we may adopt thelight-cone string field theory technique to calculate the multi-stringscattering amplitudes with an arbitrary number of external strings. We examinein detail the three-string vertex diagram and the effective four-string vertexdiagrams generated perturbatively by the three-string vertex at tree level. Inthe zero-slope limit, the string scattering amplitudes are identified preciselyas those of non-Abelian Yang-Mills gauge theory if the external states arechosen to be massless vector particles.

Covariant open bosonic string field theory on multiple D-branes in the proper-time gauge