 
Summary: DOI 10.1007/s1100500600906
Letters in Mathematical Physics (2006) 77:209218 © Springer 2006
Dispersive Calculation of the Massless Multiloop
Sunrise Diagram
ANDREAS ASTE
Department of Physics and Astronomy, Theory Division, University of Basel,
Klingelbergstrasse 82, 4056 Basel, Switzerland. email: andreas.aste@unibas.ch
Received: 10 March 2006; revised version: 7 May 2006
Published online: 15 June 2006
Abstract. The massless sunrise diagram with an arbitrary number of loops is calculated
in a simple but formal manner. The result is then verified by rigorous mathematical treat
ment. Pitfalls in the calculation with distributions are highlighted and explained. The result
displays the high energy behaviour of the massive sunrise diagrams, whose calculation is
involved already for the twoloop case.
Mathematics Subject Classification (2000). 81T05, 81T15, 81T18.
Keywords. regularization, causality, perturbative calculations.
1. Introduction
The Feynman propagator of a free massless scalar quantum field (x) fulfilling
the wave equation
2 (x)=µµ
