p-p' System with B Field and Projection Operator Noncommutative Solitons

We study the system of the Dp'-brane with Dp-brane (p<p') inside, in the case where B_{ij} field is a nonvanishing constant. In order to understand how the Dp-brane is viewed from the Dp'-brane worldvolume theory, we investigate the process in which the Dp-brane is probed with p'-p' open string. We calculate the scattering amplitudes among p-p' open strings and p'-p' open strings and show that not only the Weyl transform of the projection operator onto the ground state but also those onto higher excited states emerge as multiplicative factors of the amplitudes.