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# Communications in Number Theory and Physics

## Volume 4 (2010)

### Number 4

### Feynman amplitudes and Landau singularities for one-loop graphs

Pages: 709 – 753

DOI: http://dx.doi.org/10.4310/CNTP.2010.v4.n4.a4

#### Authors

#### Abstract

We introduce the parametric representation for Feynman integrals via configuration polynomials.We then deduce the well-known fact that massive one-loop Feynman integrals for $n$-particlescattering evaluate in terms of dilogarithms from the structure of such amplitudes as mixed Hodge structures.Analytic properties of such amplitudes are related to variations of Hodge structures and discussed in examples.