NON-ABELIAN EIKONALS

A functional formulation and partial solution is given of the non-Abel ian eikonal problem associated with the exchange of noninteracting, ch arged or colored bosons between a pair of fermions, in the large s sma ll t limit. A simple, functional ''contiguity'' prescription is devise d for extracting those terms which exponentiate, and appear to generat e the leading, high-energy behavior of each perturbative order of this simplest non-Abelian eikonal function; the lowest nontrivial order ag rees with the corresponding SU(N) perturbative amplitude, while higher -order contributions to this eikonal generate an ''effective Reggeizat ion'' of the exchanged bosons, resembling previous results for the per turbative amplitude. One exact and several approximate examples are gi ven, including an application to self-energy radiative corrections. In particular, for this class of graphs and to all orders in the couplin g, we calculate the leading-log eikonal for SU(2). Based on this resul t, we conjecture the form of the eikonal scattering amplitude for SU(N ).