TIME-DEPENDENT BACKGROUNDS IN 2-DIMENSIONAL STRING THEORY AND THE S-MATRIX GENERATING FUNCTIONAL

We study time-dependent tachyon backgrounds of the two-dimensional string collective field theory using the formalism of the S-matrix generating functional. In the process we clarify the connection between two ways of calculating the S matrix: one using the Feynman rule and the other using the classical solution to the nonlinear equation of motion. We develop the formalism for general backgrounds and apply it to the gravitational sine-Gordon model in detail. We reproduce the conformal field theory calculation which was based on expanding around the static c = 1 theory. Furthermore, we prove that the tree-level partition function of this model shows the scaling behavior corresponding to the c = 0 model in the limit p --> 0 of the sine-Gordon ''momentum'' p.