Folds, bosonization and non-triviality of the classical limit of 2D string theory

Abstract

In the 1-dimensional matrix model one identifies the tachyon field in the asymptotic region with a nonlocal transfom of the density of fermions. But there is a problem in relating the classical tachyon field with the surface profile of the Fermi fluid if a fold forms in the Fermi surface. Besides the collective field additional variables w_j(x) are required to desrcibe folds. In the quantum theory we show that the wj are the quantum dispersions of the collective field. These dispersions become O(1) rather than precisely after fold formation, thus giving additional "classical" quantities and leading to a rather nontrivial classical limit. A coherent pulse reflecting from the potential wall turns into high energy incoherent quanta (if a fold forms), the frequency amplification being of the order of the square root of the number of quanta in the incident wave.