A diagrammatic construction of formal E-independent model hamiltonian

Abstract

A diagrammatic construction of formal E-independent model interaction (i.e. without second-quantization formalism) is suggested. We start from the quasi-degenerate Brillouin-Wigner perturbation theory, in framework of which an E-dependent model hamiltonian is simply constructed. Applying the “E-removing” procedure to this E-dependent model hamiltonian, the E-independent formal model hamiltonian either hermitian or non-hermitian can be diagrammatically easily derived. For the formal E-independent model hamiltonian the separability theorem is proved, which can be profitable used for a rather “formalistic” construction of a many-body E-independent model hamiltonian containing only linked-connected diagrammatic terms.