An eikonal perturbation theory having applications in hadron dynamics. II. Massive quantum electrodynamics

Abstract

An eikonal perturbation theory (EPT), derived in previous work for a superrenormalizable coupling, is here developed for massive quantum electrodynamics (MQED) involving scalar or spinor matter fields minimally coupled to neutral massive vector gluons. After summarizing the functional method, we present the EPT for the external field problem. In agreement with results known within ordinary perturbation theory (OPT) in the eikonal approximation (EA), from an exact eikonal equation derived here we show that the EPT for the external field problem provides an excellent approximation method for Green's functions at large momenta. We then discuss some general features of the EPT for MQED, and show that it leads to a renormalizable approximation method. Our approach is then illustrated by deriving explicit expressions for various renormalized Green's functions in lowest order EPT. We also discuss some asymptotic properties of such Green's functions and indicate how to proceed with calculations in higher orders. As in our previous work, we again find that the renormalization procedure in EPT bears close resemblance to the one for OPT. Contrary to what happens with the EA, the inclusion of self-interactions and of other field-theoretic effects does not spoil the virtues of the EPT as a far better high-momenta approximation than the OPT. As a typical example, if s is an energy parameter and g the coupling constant with g 2 4π < 1 , OPT to order g 2 n often fails to be a good approximation as soon as ( g 2 4π ) ln s ∼ 1 , while in such cases EPT to order g 2 n is still a good approximation as long as ( g 2 4π ) n+1 ln s < 1 . We also find that the EPT is superior to the EA in that, contrary to the EA, it provides a step-by-step rigorous and renormalizable iterative approximation method which can account for self-interactions and other field-theoretic effects. We emphasize that the EPT is much simpler and more general than other explicit approximate summation methods of classes of OPT Feynman graphs. In field theory, we consider the use of the EPT as a generalization of the EA for discussing, e.g. high-energy behaviors in MQED as well as infrared divergence and bound-state problems in the limit of massless gluons. It is also suggested that, in view of its nice field-theoretic and high-energy properties, the EPT for MQED might provide a useful laboratory where ideas and problems in hadron dynamics could be meaningfully investigated within a Lagrangian field theory.