Abstract
We consider the quantization of Liouville's equation in a box, with appropriate boundary conditions, as comes out of Polyakov's analysis of the Nambu action. The answer to this problem gives the spectrum of the dual string in this new approach. In this first paper, we concentrate mostly on the classical theory, including the inverse scattering method, which are needed to separate the modes, a prerequisite to an exact canonical quantization. In particular, we point out the important role of a parameter appearing in the boundary conditions, which depends on the space-time dimension, and we show that the system reduces to an involved set of harmonic oscillators.
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