Functional integral methods in the theory of the Anderson model

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Abstract
The use of the functional integration technique applied to the problem of local moment formation in the Anderson model is reviewed in this paper. The different approximations are discussed, in order to clarify both their internal consistency and relations among them. Connection with the ordinary diagrammatic approach is made by summarizing and extending previous treatments done on this subject; and the difference between the one-field and the two-field approaches is explained in terms of the ‘unphysical diagrams’ generated by the first. The results for the magnetic susceptibility are presented for each approximation discussed in the paper, both in the strong magnetic and in the non-magnetic regime; while it is shown that no reliable approximation has been developed for the intermediate coupling situation. Finally the Kondo effect is discussed within the functional integration scheme and application of the method to the study of superconducting magnetic alloys is reviewed.