The projected single-particle Dirac operator for Coulombic potentials
Documenta mathematica, Tome 10 (2005), pp. 331-356
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 Λ+AΛ++Λ−AΛ− to any given order in the potential strength, where Λ+ and Λ− project onto the positive and negative spectral subspaces of the free Dirac operator. To first order, Λ+AΛ+ coincides with the Brown-Ravenhall operator. Moreover, there exists a simple relation to the Dirac operator transformed 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 potential, V=−γx−1+ε,ε>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.
@article{10_4171_dm_191,
author = {D.H. Jakubassa-Amundsen},
title = {The projected single-particle {Dirac} operator for {Coulombic} potentials},
journal = {Documenta mathematica},
pages = {331--356},
year = {2005},
volume = {10},
doi = {10.4171/dm/191},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/191/}
}
D.H. Jakubassa-Amundsen. The projected single-particle Dirac operator for Coulombic potentials. Documenta mathematica, Tome 10 (2005), pp. 331-356. doi: 10.4171/dm/191
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