Dynamical Lie algebra and conditional operators for many fermion Green functions

A method is introduced to calculate thermodynamic Green functions. A powerful theorem by Masson is the motivation for expressing the Fourier-time transform of the Green function as a super space matrix element of the resolvent of the Liouville operator. The eigenvalues of the Liouville operator are then expressed in a form first suggested by Judd for atomic systems and which are shown to be members of a Lie group.