Abstract
5. Conclusions It follows from the results of Sects. 2 and 3 that there is no significant change in the value of the cross sections when the external static magnetic dipole field is represented by a vector potential rather than by a scalar one. Our first order calculations are in good agreement with those of De Logi and Mickelson (7) once all normalization factors are recovered. The difference in the expression of Ginzburg and Tsytovich (6) is attributable to their use of an incorrect expression for the fields of the dipole. Obviously, as in the scalar case, the cross section does not depend on Planck's constant since the interaction has a classical limit. The TT-gauge greatly facilitates the calculations of the radiative corrections which are then restricted to the sole contribution of the two vertex diagrams. This substantiates the arguments advanced by De Logi and Mickelson (6) in favour of the use of this gauge in external field problems. In a different gauge both the two and three vertex diagrams must be calculated and then added. Because of the assumed approximate gravitational gauge invariance to this order, the results would, however, have to agree within the limits of the approximation. In Sect. 4 we have improved our previous estimate of the radiative corrections for an external Coulomb field.
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