A self-consistent dynamical theory is presented for the Anderson lattice. In a variational Lagrangian formulation a trial conduction-electron propagator is introduced. A variational principle leads to optimization of the propagator with the accuracy of O 1 2 where zn is the number of interacting neighbors. The extended non-crossing approximation (XNCA) is reproduced as a special case of the present theory. An integral equation is obtained for the dynamical susceptibility which incorporates the RKKY interaction and the Kondo effect. The closed-form solution is given in a case where perturbation theory is applicable.
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