An infinite-dimensional classical integrable system and the Heisenberg and Schrödinger representations

Abstract

We present an infinite-dimensional classical integrable hamiltonian system on projective Hilbert space. We show that the equations of motion correspond to the Heisenberg ones of quantum mechanics when the hamiltonian operator is compact, and that the formulation of these equations as a classical Lax pair with parameter gives rise naturally to an infinite set of conversation laws. Further, an infinite-dimensional version of Moser's transformation for integrating classical systems is shown to relate the Heisenberg and Schrödinger pictures.