Study of the longitudinal kink modes of the string

Abstract

We examine the massless limit of a model for the massive relativistic Nambu string. The system possesses longitudinal kink modes excluded from the standard lightlike gauge treatment. We demonstrate the equivalence of these modes to those proposed by Patrascioiu. The classical nonlinear field theory of the two-dimensional string is shown to be a completely integrable Hamiltonian system. The Hamiltonian is expressed in terms of normal-mode action variables alone; the mass-squared spectrum is linear in the Bohr-Sommerfeld approximation. The difficulties of canonical quantization are exposed using a particular timelike gauge which admits commuting center-of-mass coordinates.