Generalized creation and annihilation operators: Physical interpretation and reordering properties

Matrix elements for fermion and boson operators describing the creation or annihilation of particles with multiple angular-momentum quantum numbers can be factored into products of matrix elements of generalized operators, one for each quantum number. The generalized operators have nonzero matrix elements between states of arbitrary permutational symmetry. This factorization greatly increases the efficiency of shell-model calculations. We provide a physical interpretation for these generalized operators and introduce a simple operator-reordering procedure