On the functional integral approach in quantum statistics: I. Some approximations

The susceptibility of a Kondo system in a fairly wide temperature region is calculated in the first-harmonic approximation in a functional integral approach. The comparison with the value obtained by renormalization group theory shows that in this region the two results agree quite well. The expansion of the partition function with infinite independent harmonics for the Anderson model is studied. Some symmetry relations are generalized. It is a challenging problem to develop a functional integral approach including diagram analysis, mixed-mode effects and some exact relations in the Anderson system proved in a functional integral approach. These topics will be discussed in a subsequent paper.