Matrix elements of many-body operators and density correlations.

C. Brouder (1)

1 IMPMC - Institut de minéralogie et de physique des milieux condensés

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)[centered ellipsis]n(xk):, where n(x)=psi[dagger](x)psi(x) is the density operator. The relation between the split-and-pair method and quantum group theory is clarified.

Mots clés: matrix algebra; group theory; quantum theory

C. Brouder. Matrix elements of many-body operators and density correlations.. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2005, 72, pp.032720(1-11). ⟨10.1103/PhysRevA.72.032720⟩. ⟨hal-00020031⟩