Analytic Properties of Triangle Feynman Diagrams in Quantum Field Theory

TL;DR

This paper investigates the analytic structure of triangle Feynman diagrams in quantum field theory, focusing on dispersion representations and the emergence of anomalous singularities and cuts.

Contribution

It provides a detailed analysis of dispersion representations for triangle diagrams, highlighting the role of anomalous singularities and cuts in their analytic properties.

Findings

Derived single and double dispersion representations for triangle diagrams

Identified conditions for anomalous singularities and cuts

Enhanced understanding of analytic structure in quantum field theory

Abstract

We discuss dispersion representations for the triangle diagram $F(p_1^2,p_2^2,q^2)$, the single dispersion representation in $q^2$ and the double dispersion representation in $p_1^2$ and $p_2^2$, with special emphasis on the appearance of the anomalous singularities and the anomalous cuts in these representations.