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DOI 10.1007/s11005-007-0169-8 Letters in Mathematical Physics (2007) Springer 2007

Summary: DOI 10.1007/s11005-007-0169-8
Letters in Mathematical Physics (2007) © Springer 2007
Resummation of Mass Terms in Perturbative
Massless Quantum Field Theory
Department of Physics and Astronomy, University of Basel, Klingelbergstrasse 82,
4056 Basel, Switzerland. e-mail: andreas.aste@unibas.ch
Received: 24 May 2007 / Accepted: 30 June 2007
Abstract. The neutral massless scalar quantum field in four-dimensional space-time is
considered, which is subject to a simple bilinear self-interaction. Is is well-known from
renormalization theory that adding a term of the form -m2
2 to the Lagrangean has
the formal effect of shifting the particle mass from the original zero value to m after
resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative
expansion of the S-matrix. 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,


Source: Aste, Andreas - Institut für Physik, Universität Basel


Collections: Physics