Frozen and Broken Color : a Matrix Schroedinger Equation in the Semiclassical Limit

e consider a simple one-dimensional theory in which a colored spinless quark and antiquark are bound together by a confining, colordependent potential. Our purpose is to investigate in more detail the dynamics underlying Lipkin's mechanism of hidden charge, and how his conclusions are modified in the presence of symmetry breaking. We consider the case of "frozen color", i.e. where global color symmetry remains exact, but where colored states have a mass large compared to color-singlet mesons. Using semiclassical WJB formalism, we construct the spectrum of bound states. In order to determine the charge of the constituents , we then consider deep-inelastic scattering of an external probe (e.g. lepton) from our one-dimensional meson. We calculate explicitly the structure function, W, in the WKB limit and show how Lipkin's mechanism is manifested, as well as how scaling behavior comes about. The dominant physical process is one of excitation of a semiclassical state by the hard collision of the probe with the quark or antiquark. We generalize these considerations to the case of broken color symmetry but where the breaking is not so strong as to allow lowlying states to have a large amount of mixing with the colored states. In this case, the degeneracy of excited colored states can-be broken. The WKB approximation again suffices to provide a description of the spectra. Again deep-inelastic scattering can be used to measure the charges of the constituents, and there will again be a distinct contribution from each type of "classical" state which can be excited by