Implementing Unitarity in Perturbation Theory

Details Implementing Unitarity in Perturbation Theory Implementing Unitarity in Perturbation Theory

2001-03-13

arxiv.org/abs/hep-ph/0103143v2

Phys.Rev. D63 (2001) 097901

Physics

High Energy Physics

High Energy Physics - Phenomenology

to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.63.097901

Unitarity cannot be perserved order by order in ordinary perturbation theory because the constraint $UU^\dagger=\1$ is nonlinear. However, the corresponding constraint for $K=\ln U$, being $K=-K^\dagger$, is linear so it can be maintained in every order in a perturbative expansion of $K$. The perturbative expansion of $K$ may be considered as a non-abelian generalization of the linked-cluster expansion in probability theory and in statistical mechanics, and possesses similar advantages resulting from separating the short-range correlations from long-range effects. This point is illustrated in two QCD examples, in which delicate cancellations encountered in summing Feynman diagrams of are avoided when they are calculated via the perturbative expansion of $K$. Applications to other problems are briefly discussed.

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