Phase averaging and generalized eikonal representations

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Abstract
A new, ‘‘phase-averaged’’ approximation to the coupled Green’s functions of potential theory and quantum field theory is shown to lead to generalized eikonal approximations in which the nonperturbative effects of low-frequency virtual quanta can be extracted and represented for all processes, including determinantal factors not necessarily associated with particle scattering, in terms of a finite number of quadratures, depending on the interaction, the number of space-time dimensions, and the process considered. Derivations and discussions are given for potential theory and scalar and gauge field theory.