Electric properties regular approximation

Since we can regard the regular approximation as a Foldy-Wouthuysen transformation, we should be able to use a similar line of development for the property operators as in chapter 16. There we found that it was relatively easy to deal with the electric perturbations because they appeared as powers of the perturbation operator, with a linear operator at lowest order. The magnetic perturbations, on the other hand, were much more complicated because the transformation involved complicated functions of the momentum, which must be replaced with the expression that includes the vector potential. 

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