Explicit Expressions of the Positive-Energy Hamiltonians

Up to this point all Hamiltonians that have been derived still belong to the four-component world and therefore possess a 2 x 2 superstructure. Moreover, they have been presented in a compact commutator notation, which still involves the antihermitean operators Wj. These operators cannot be calculated 

For the sake of brevity, we stick to the notation fioKHn also for the (2x2)-block diagonal operators (up to this point, these operators denoted sums of block-diagonal (4x4) even operators). Up to fourth-order (n=4), the (2x2)-dimensional DKH Hamiltonians 

The electronic, i.e., upper-left (2 x 2)-blocks of the kernels of the lowest-order terms may be explicitly given as 

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