Two-pearl Strings: Feynman's Oscillators

Abstract

String models are designed to provide a covariant description of internal space-time structure of relativistic particles. The string is a limiting case of a series of massive beads like a pearl necklace. In the limit of infinite-number of zero-mass beads, it becomes a field-theoretic string. Another interesting limit is to keep only two pearls by eliminating all others, resulting in a harmonic oscillator. The basic strength of the oscillator model is its mathematical simplicity. This encourages us to construct two-pearl strings for a covariant picture of relativistic extended particles. We achieve this goal by transforming the oscillator model of Feynman {\it et al.} into a representation of the Poincar\'e group. We then construct representations of the O(3)-like little group for those oscillator states, which dictates their internal space-time symmetry of massive particles. This simple mathematical procedure allows us to explain what we observe in the world in terms of the fundamental space-time symmetries, and the built-in covariance of the model allows us to use the physics in the rest frame in order to explain what happens in the infinite-momentum frame. It is thus possible to calculate the parton distribution within the proton moving light-like speed in terms of the quark wave function in its rest frame.