We show that the quantum linear harmonic oscillator can be obtained in the
large N limit of a classical deterministic system with SU(1,1) dynamical
symmetry. This is done in analogy with recent work by G.'t Hooft who
investigated a deterministic system based on SU(2). Among the advantages of our
model based on a non--compact group is the fact that the ground state energy is
uniquely fixed by the choice of the representation.Comment: 4 pages, 2 figures, minor corrections added. To appear in the
Proceedings of Waseda International Symposium on Fundamental Physics: "New
Perspectives in Quantum Physics", 12-15 November 2002, Waseda University,
Tokyo, Japa
