Letters in Mathematical Physics

, Volume 108, Issue 5, pp 1147–1162 | Cite as

Loop vertex expansion for higher-order interactions

  • Vincent RivasseauEmail author


This note provides an extension of the constructive loop vertex expansion to stable interactions of arbitrarily high order, opening the way to many applications. We treat in detail the example of the \((\bar{\phi } \phi )^p\) field theory in zero dimension. We find that the important feature to extend the loop vertex expansion is not to use an intermediate field representation, but rather to force integration of exactly one particular field per vertex of the initial action.


Quantum field theory Constructive field theory Loop vertex expansion 

Mathematics Subject Classification




We thank G. Duchamp, R. Gurau, L. Lionni and A. Sokal for useful discussions.


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Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique, CNRS UMR 8627Université Paris XIOrsay CedexFrance

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