CLASSICAL INTEGRABILITY AND HIGHER SYMMETRIES OF COLLECTIVE STRING FIELD-THEORY

We demonstrate the complete integrability of classical collective field theory. An exact equivalence to the classical N-body problem of Calogero type is described. A Lax pair is constructed for the general continuum collective equations. A form of background independence is pointed out. An infinite set of commuting currents is constructed in the general case. A large symmetry algebra is discovered and shown to take the form of a W infinity algebra.