Dynamics Underlying Duality and Gauge Invariance in the Dual-Resonance Models

Abstract

Making use of the similarity between the factorized spectrum of the generalized beta function and the spectrum of a vibrating string in Minkowski space, we construct a formalism within which we give a geometrical interpretation to the gauge symmetries inherent in the theory. The key point in the construction is the identification of the harmonic-oscillator amplitude with the components of actual coordinates in space-time. It turns out that these coordinates must satisfy certain constraints arising from purely geometrical considerations, and these constraint equations are then shown to be the familiar gauge conditions on the underlying states. Analogies with more familiar gauge theories are pointed out.