Bound states in field theory from confinement and asymptotic behavior

Abstract

A method of successive approximations is developed that allows the calculation of bound states of confined relativistic or nonrelativistic quantum systems from asymptotic behavior and analyticity. The accuracy of the approximation increases rapidly as the asymptotic behavior is given to larger and larger inverse powers of energy. Because of a special scaling property the method is applicable for systems with many bound states, independent of the strength of the coupling. The method is successfully tested in potential theory for the harmonic-oscillator potential. Application to quantum chromodynamics is discussed where the renormalization group in principle permits the determination of the asymptotic behavior.