NUCLEAR Nuclear Physics B 376 (1992) 75—98 P HY S I CS B North-Holland Non-perturbative collective field theory * Antal Jevicki Department of Physics, Brown University, Providence, RI 02912, USA Received 1 July 1991 (Revised 23 December 1991) Accepted for publication 30 December 1991 We present a non-perturbative framework for collective field theory. Two methods are given. In the first exact Fock space states diagonalizing the hamiltonian are described. Based on these, effective lagrangians are introduced. An extra single-particle branch is pointed out. It is shown that the states of this new branch correspond to solitons, the semiclassical soliton solutions are seen to take the form of a single eigenvalue effect. In general we argue that single (complex) eigenvalues will lead to solitons while real eigenvalues give instanton configurations. 1. Introduction There has been significant progress in understanding of lower-dimensional string theories [1—5].At present the theory with a most interesting physical structure is that for D = 1 which represents c = 1 matter coupled to two-dimen- sional gravity [3,5,9]. It has a non-trivial physical spectrum consisting of a massless tachyon and possibly other states. The collective theory of refs. [3,4] offers a field theoretic framework for one-dimensional strings. It is based on a scalar field but contains structure which could possibly give a complete theory of closed strings. Its properties have been investigated in some detail recently [6—11].Perturbative calculations were per- formed [7,81 giving expressions for scattering amplitudes. These are seen [71 to contain poles exhibiting an infinite sequence of discrete states [13,14]. It is clear that there are very interesting physical phenomena which have non-perturbative origin [15,16]. One has, furthermore, the possibility of under- * Work supported in part by the Department of Energy under contract DE-ACO2-76ER03 130-Task A. 0550-3213/92/$05.00 © 1992 — Elsevier Science Publishers B.V. All rights reserved