Abstract
By adapting the proper-time method to both the electromagnetic and Dirac fields in interaction with a weak vierbein field, bein gauge is treated on an equal footing with coordinate gauge. The calculations of the local one-photon as well as the second- and first-order-differential one-electron Green functions are developed in terms of the first-order vierbein and auxiliary fields and the weak-field potentials, and are shown to exhibit manifest coordinate- and bein-gauge covariance. The gauge separations of the first-order fields allow the isolation and evaluation of the contributions from both the coordinate- and bein-gauge functions, permit expressions of the first-order contributions to the Green functions in terms of the gauge-invariant weak-field potentials, and lead to the modified versions of the Mandelstam-DeWitt path-dependent line integrals.
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