 
Summary: DOI 10.1007/s1100500701698
Letters in Mathematical Physics (2007) © Springer 2007
Resummation of Mass Terms in Perturbative
Massless Quantum Field Theory
ANDREAS ASTE
Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82,
4056 Basel, Switzerland. email: andreas.aste@unibas.ch
Received: 24 May 2007 / Accepted: 30 June 2007
Abstract. The neutral massless scalar quantum field in fourdimensional spacetime is
considered, which is subject to a simple bilinear selfinteraction. Is is wellknown from
renormalization theory that adding a term of the form m2
2
2 to the Lagrangean has
the formal effect of shifting the particle mass from the original zero value to m after
resummation of all twoleg insertions in the Feynman graphs appearing in the perturbative
expansion of the Smatrix. However, this resummation is accompanied by some subtleties
if done in a proper mathematical manner. Although the model seems to be almost triv
ial, is shows many interesting features which are useful for the understanding of the con
vergence behavior of perturbation theory in general. Some important facts in connection
with the basic principles of quantum field theory and distribution theory are highlighted,
