Summary: DOI 10.1007/s11005-006-0090-6
Letters in Mathematical Physics (2006) 77:209218 © Springer 2006
Dispersive Calculation of the Massless Multi-loop
Department of Physics and Astronomy, Theory Division, University of Basel,
Klingelbergstrasse 82, 4056 Basel, Switzerland. e-mail: email@example.com
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 two-loop case.
Mathematics Subject Classification (2000). 81T05, 81T15, 81T18.
Keywords. regularization, causality, perturbative calculations.
The Feynman propagator of a free massless scalar quantum field (x) fulfilling
the wave equation