Advances in Mathematical Physics
Volume 2009 (2009), Article ID 180159, 12 pages
Review Article

Constructive Field Theory in Zero Dimension

Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris XI, 91405 Orsay Cedex, France

Received 28 June 2009; Accepted 29 September 2009

Academic Editor: M. N. Hounkonnou

Copyright © 2009 V. Rivasseau. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Constructive field theory can be considered as a reorganization of perturbation theory in a convergent way. In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zero-dimensional ϕ4 field theory, in increasing order of sophistication and power.