ZERO MODE DIVERGENCE PROBLEM IN STRING THEORY

For 2D string theory, the perturbative S-matrices are not well-defined due to a zero mode divergence. Although there exist formal procedures to make the integral convergent, their physical meanings are not clea r. We describe a method to obtain finite S-matrices physically to just ify the formal schemes. The scheme uses asymptotic states by wave pack ets which fall faster than exponentials. It is shown that the scheme g ives well-defined S-matrices and justifies the formal shifted Virasoro -Shapiro amplitude for simple processes. The tree-level unitarity for these processes is also shown. We point out a problem in this scheme.