 
Summary: DOI 10.1007/s1100500601133
Letters in Mathematical Physics (2006) 78:157172 © Springer 2006
Causal Construction of the Massless Vertex
Diagram
ANDREAS ASTE
Department of Physics and Astronomy, Theory Division, University of Basel,
Klingelbergstrasse 82, 4056 Basel, Switzerland. email: andreas.aste@unibas.ch
Received: 17 July 2006; revised version: 25 August 2006
Published online: 28 September 2006
Abstract. The massless oneloop vertex diagram is constructed by exploiting the causal
structure of the diagram in configuration space, which can be translated directly into dis
persive relations in momentum space.
Mathematics Subject Classification (2000). 81T05, 81T15, 81T18.
Keywords. causality, perturbative calculations, Feynman diagrams.
1. Introduction
In the traditional approach to quantum field theory, one starts from classical fields
and a Lagrangean which describes the interaction. These objects get quantized
and Smatrix elements or Greens functions are constructed with the help of the
Feynman rules. A typical example which is used in this paper as a model theory is
the massless 3theory, where the interaction Hamiltonian density is given by the
