00-101 Detlef Lehmann

Resummation of Feynman Diagrams and the Inversion of Matrices (109K, LaTeX 2e with 4 PS Figures) Mar 6, 00

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Abstract. In many field theoretical models one has to resum two- and four-legged subdiagrams in order to determine their behaviour. In this article we present a novel formalism which does this in a nice way. It is based on the central limit theorem of probability and an inversion formula for matrices which is obtained by repeated application of the Feshbach projection method. We discuss applications to the Anderson model,to the many-electron system and to the phi^4-model. In particular, for the many-electron system with attractive delta-interaction, we find that the expectation value of the Hubbard-Stratonovich field for small momentum q has a delta-function singularity instead of the commonly expected 1/q^2 type singularity.

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