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

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

2004-10-04

arxiv.org/abs/math/0410050v4

Mathematics

Analysis of PDEs

28 pages, 5 figures

Scientific paper

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.

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