Moving Branes in Presence of the Background Tachyon Fields

We compute the boundary state associated with a moving D$p$-brane in the presence of the open string tachyon field as a background field. The effect of the tachyon condensation on the boundary state will be discussed. It leads to a boundary state associated with a lower dimensional moving D-brane or a stationary instantonic D-brane. The former originates from condensation along the spatial directions and the latter comes from the temporal direction of the D-brane's worldvolume. Using the boundary state we also study the interaction amplitude between two arbitrary D$p_1$ and D$p_2$-branes. The long range behavior of the amplitude is investigated which shows an obvious deviation from the conventional form, due to the presence of the background tachyon field.