Abstract:
A relativistic string is described by the inverse scattering method for periodic
potentials. The auxiliary spectral problem and the analytic properties of the
Bloch functions are investigated. A complete set of involutive relativistieally
invariant integrals of the motion is obtained. Equations are obtained for string
configurations that have a finite number of gaps in the spectrum of the auxiliary
problem. It is shown that such a condition is equivalent to stationarity of the
configurations with respect to the higher string equations. The quantum theory
in the single-gap sector is discussed.
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