YANGIAN-INVARIANT FIELD-THEORY OF MATRIX-VECTOR MODELS

We extend our study of the field-theoretic description of matrix-vecto r models and the associated many-body problems of one dimensional part icles with spin, We construct their Yangian-su(R) invariant Hamiltonia n. It describes an interacting theory of a c = 1 collective boson and a k = 1 su(R) current algebra. When R greater than or equal to 3 cubic -current terms arise, Their coupling is determined by the requirement of the Yangian symmetry. The Hamiltonian can be consistently reduced t o finite-dimensional subspaces of states, enabling an explicit computa tion of the spectrum which we illustrate in the simplest case.