Rotation and the Dirac Equation

We start from the Dirac one-particle Hamiltonian for an electron bound to a point nucleus 

The scaling of the radial coordinate with a complex constant, eie, as in Eq. (8) gives then the scaled Hamiltonian 

When working on a positive energy solution, the operators A+ give unity, but on a negative energy solution, they give zero. The eigenstates to a matrix representation of Eq. (40) can conveniently be used to express the A operators. The electron-electron interaction operator, V12/ is dominated by the Coulomb interaction, which when complex rotation is used is written 

In addition, V 2 should include corrections due to the finite speed of the electromagnetic interaction, as well as magnetic contributions present due to the electron spin. An approximate way to account for these effects, correct to order a2 a.u., is provided by the Breit operator [115] 

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