Kadanoff-Baym equations

These equations are important for solving Kadanoff-Baym equations. 

The external potential is included in these equations. The self-energy is defined as a function or operator in the Keldysh space according to Eq. (20). obeys the Kubo-Martin-Schwinger boundary conditions (16). The ( )-projections of the Kadanoff-Baym equations can written as... 

Lipavsky, P., Spicka, V. and Velicky, B. (1986) Generalized Kadanoff-Baym Ansatz for Deriving Quantum Transport-Equations. Phys. Rev. B, 34, 6933-6942. 

Physics described by the model with so many parameters is very rich and the model is able particularly to treat heavy fermion systems. To study the model many approaches were suggested (see reviews [2-5]). They are successful for particular regions of the parameter space but no one is totally universal. In this paper we apply to PAM the generating functional approach (GFA) developed first by Kadanoff and Baym [6] for conventional systems and generalized for strongly correlated electron systems [7-10]. In particular it has been applied to the Hubbard model with arbitrary U in the X-operators formalism [10]. The approach makes it possible to derive equations for the electron Green s function (GF) in terms of variational derivatives with respect to fluctuating fields. 

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