Interactions and scattering in d = 1 string theory

Abstract

We discuss two results: (i) we calculate the two-point function of the density fluctuations to ^O(g²_st) in the fermonic formulation of the d = 1 string theory and compare with the ^O(g²_st) result from the candidate collective field Hamiltonian. The latter result is divergent, showing the inequivalence of the two theories. We find out the corrections to the collective field Hamiltonian (both in the form of infinite counterterms and additional finite pieces) needed to match with the fermion theory. (ii) We study tree-level scattering processes between bosons due to the localized interaction near the boundary (in a region of order √α ¹ ). The reflection problem at the boundary is treated by an analytic continuation of the time-of-flight variable.