Bound states and asymptotically free quarks

Abstract

We prove duality relations between bound states and asymptotically free quarks by using relativistic wave functions and couplings to currents. Our approximation is based on WKB formulas and on an ansatz on the potential at very small distances, where the instantaneous potential approximation for the Bethe-Salpeter equation is unreliable. We apply our results to two-point spectral functions of vector and axial-vector currents.