Schwinger's Proper-Time Method and the Eikonal Approximation

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Abstract
Eikonal techniques are used to present an alternative treatment of the electron's Green's function in the presence of a plane-wave field. After studying the propagation of an electron in a prescribed electromagnetic field we eikonalize the corresponding Green's function. If the external field is chosen to be a laser field, the approximate eikonal propagator is turned into an exact one: Additional assumptions characterizing the eikonal approximation are automatically satisfied. The methods employed are Schwinger's pre-source-theory functional techniques.