Matrix elements of many-body operators and density correlations

The matrix element of a general many-body operator between two Slater determinants is calculated explicitly. For this, a split-and-pair method is introduced that provides a convenient expression of Wick's theorem and simplifies many-body calculations. The same method is used to determine the generating function of the matrix elements of many-body operators. The split-and-pair method allows also for the diagonalization of the density correlation operators :n(x1)···n(xk):, where n(x)=ψ†(x)ψ(x) is the density operator. The relation between the split-and-pair method and quantum group theory is clarified