Diagram technique for the Hubbard model

A generalized Wick theorem is formulated for the Hubbard model. According to the theorem, the mean value of the time-ordered product of electron operators is represented as a sum of products of single-site cumulants. The theorem is used to construct a diagram technique for the temperature-dependent Green's functions. A Dyson equation for the single-particle Green's function and an expression for the free energy are obtained.