title: Simplified diagrammatic expansion for effective operators.
abstract: For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams, and evaluation rules from effective transition operators that give exact transition matrix elements between effective eigenvectors in reduced model space. By modifying these diagrams slightly and considering the linked diagrams for all the terms of the same order, we find that the evaluation rules can be made the same for both effective Hamiltonian and effective transition operator diagrams, and in many cases it is possible to combine many diagrams into one modified diagram. We give the rules to evaluate these modified diagrams and show their validity.
authors.affiliation: Institute of Applied Physics and College of Electronic Engineering, Chongqing University of Post and Telecommunications, Chongqing 400065, China.
authors.forename: Chang-Kui
authors.initials: CK
authors.lastname: Duan
authors.forename: Yun-Gui
authors.initials: YG
authors.lastname: Gong
authors.forename: Hui-Ning
authors.initials: HN
authors.lastname: Dong
authors.forename: Michael F
authors.initials: MF
authors.lastname: Reid