in nature. It is this point of view that we shall adopt in the present article.

Such an approach should be distinguished from the problem of studying single-string scattering of a $D$-particle with closed string states in flat space times [@paban]. We have shown in [@kogan; @kmw; @szabo; @recoil] that for a $D$-particle embedded in a $d$-dimensional [*flat Minkowski*]{} space time such an impulse action is described by a world-sheet $\sigma$-model deformed by appropriate ‘recoil’ operators, which obey a logarithmic conformal algebra [@lcft]. The appearance of such algebras, which lie on the border line between conformal field theories and general renormalizable field theories in the two-dimensional world sheet, but can still be classified by conformal data, is associated with the fact that an impulse action (recoil) describes a [*change*]{} of the string/D-particle background, and as such it cannot be described by conformal symmetry all along. The [*transition*]{} between the two asymptotic states of the system before and (long) after the event is precisely described by deforming the associated $\sigma$-model by operators which [*spoil*]{} the conformal symmetry.

Indeed, the recoil operators are [*relevant*]{} from a world-sheet renormalization-group view point [@kmw], and thus the induced string theory becomes non-critical, in need of 