Wick’s theorem and reconstruction schemes for reduced density matrices

We first obtained a closed form of the Wick’s theorem expressed in Grassman wedge product, which is similar to a binomial expansion. With this new expansion, new reconstruction schemes for reduced density matrices are derived rigorously. The higher order reduced density matrices are systematically decomposed into a sum of the lower order reduced density matrices which could be used to solve the contracted Schr?dinger equation.