General Structure of Effective Interaction in Degenerate Perturbation Theory

Abstract

A general definition of effective Hamiltonian or effective interaction is given, which includes the standard non-Hermitian form, Kato's effective Hamiltonian and the Hermitian form as special cases. A classification rule for various effective Hamiltonians is established. General and exact expansion formulae are given for the wave operator and the effective interactions including the Hermitian form in the case that unperturbed energies are degenerate.