INCLUSION OF FERMIONIC DEGREES OF FREEDOM IN THE LATTICE-DYNAMICS SHELL-MODEL

We present a model which allows us to describe not only the interaction of electrons with rigid ions, but also the interaction between electrons and the deformation of the electronic clouds of the ions due to atomic displacements. To this purpose the usual shell model is extended by incorporating a finite set of fermionic coordinates (Grassmann variables), which represent the fermionic degrees of freedom. The pseudomechanics and the quantum statistical mechanics of the model are studied. The perturbative formalism for a general interacting potential and the Feynman rules are given. This perturbative method is useful to evaluate several physical properties in solid state physics at finite temperature.