BRST quantization of noncommutative gauge theories

In this paper, the Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformation is presented for the noncommutative $\mathrm{U}\mathrm{}\left(N\right)\mathrm{}$ gauge theory. The nilpotency of the charge associated with this symmetry is then proved. As a consequence of the spacelike noncommutativity parameter, the Hilbert space of physical states is determined by the cohomology space of the BRST operator as in the commutative case. Further, the unitarity of the S-matrix elements projected onto the subspace of the physical states is deduced.