# Planar Binary Trees and Perturbative Calculus of Observables in Classical Field Theory

Abstract : Consider the Klein-Gordon equation coupled with an interaction term $(\Box+m^2)\phi+\lambda\psi^p$. For the linear Klein-Gordon equation, a kind of generalized Noether's theorem gives us a conserved quantity. The purpose of this paper is to find an analogue of this conserved quantity in the interacting case. We see that it can be done perturbatively, and we define explicitely a conserved quantity using a perturbative expansion based on Planar Binary Tree and a kind of Feynman rules. Only the case $p=2$ is treated but our approach can be generalized to any $\phi^p$-theory.
Mots-clés :
Type de document :
Pré-publication, Document de travail
28 pages, 5 figures. 2005
Domaine :

https://hal.archives-ouvertes.fr/hal-00020097
Contributeur : Dikanaina Harrivel <>
Soumis le : lundi 6 mars 2006 - 10:12:03
Dernière modification le : mercredi 19 décembre 2018 - 14:08:04

### Citation

Dikanaina Harrivel. Planar Binary Trees and Perturbative Calculus of Observables in Classical Field Theory. 28 pages, 5 figures. 2005. 〈hal-00020097〉

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