A new technique for computing the spectral density of sunset-type diagrams: integral transformation in configuration space

Abstract

We present a new method to investigate a class of diagrams which generalizes the sunset topology to any number of massive internal lines. Our attention is focused on the computation of the spectral density of these diagrams which is related to many-body phase space in $D$ dimensional space-time. The spectral density is determined by the inverse $K$-transform of the product of propagators in configuration space. The inverse $K$-transform reduces to the inverse Laplace transform in any odd number of space-time dimensions for which we present an explicit analytical result.