 00101 Detlef Lehmann
 Resummation of Feynman Diagrams and the Inversion of Matrices
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Mar 6, 00

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Abstract. In many field theoretical models one has to resum two and fourlegged
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 manyelectron system and to the phi^4model. In particular, for
the manyelectron system with attractive deltainteraction,
we find that the expectation value of the HubbardStratonovich field
for small momentum q has a deltafunction singularity instead of
the commonly expected 1/q^2 type singularity.
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