Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure

A diagonalisation procedure of the Foldy-Wouthuysen type is considered for the single-electron Dirac Hamiltonian as a basis for many-body applications. A modified procedure is suggested. In the diagonalisation procedure the Dirac equation is completely decoupled into two equations of the Pauli type. The expressions for positive- and negative-energy projection operators in the transformed basis are then trivial and, by performing the inverse transformation, projection operators for Dirac functions are obtained. Applying a similar transformation to the two-electron Dirac-Coulomb Hamiltonian leads to a diagonalised single-electron part and a non-diagonal two-electron interaction. In principle, the effect of the exchange of virtual, transverse photons (Breit interactions) can also be included in the electron-electron interaction and transformed in a similar way. It is indicated how a diagonalisation procedure of this kind can be used as a basis for relativistic many-body calculations in the coupled cluster formulation in analogy with the corresponding non-relativistic procedure.

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