经典域论中的平面二叉树与观测量微扰演算
Planar Binary Trees and Perturbative Calculus of Observables in Classical Field Theory
摘要：
考虑与相互作用项$(\Box+m^2)ϕ+λψ^p$耦合的Klein-Gordon方程。对于线性Klein-Gordon方程，一种推广的Noether定理给出了一个守恒量。本文的目的是在相互作用的情况下找到这个守恒量的类似物。我们看到它可以微扰地完成，我们明确地定义了一个守恒量的微扰展开的基础上的平面二叉树和一种费曼规则。只有情况$p=2$的治疗，但我们的方法可以推广到任何$ϕ^p$ -理论。
英文摘要：
Consider the Klein-Gordon equation coupled with an interaction term $(\Box+m^2)ϕ+λψ^p$. 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 $ϕ^p$-theory.
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