Abstract
A sequence of unitary transformations is applied to the one-electron Dirac operator in an external Coulomb potential such that the resulting operator is of the form ¤+A ¤+ + ¤−A ¤− to any given order in the potential strength, where ¤+ and ¤− project onto the positive and negative spectral subspaces of the free Dirac operator. To first order, ¤+A ¤+ coincides with the Brown-Ravenhall operator. Moreover, there exists a simple relation to the Dirac operator trans- formed with the help of the Foldy-Wouthuysen technique. By defining the transformation operators as integral operators in Fourier space it is shown that they are well-defined and that the resulting transformed operator is p-form bounded. In the case of a modified Coulomb po- tential, V = −γx −1+ǫ , ǫ > 0, one can even prove subordinacy of the n-th order term in γ with respect to the n − 1st order term for all n > 1, as well as their p-form boundedness with form bound less than one.
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