Renormalization of composite operators

Details Renormalization of composite operators Renormalization of composite operators

2000-11-10

arxiv.org/abs/hep-th/0011083v2

Phys.Rev. D63 (2001) 105006

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, revtex (accepted by Phys. Rev. D), changes in introduction and summary

Scientific paper

10.1103/PhysRevD.63.105006

The blocked composite operators are defined in the one-component Euclidean scalar field theory, and shown to generate a linear transformation of the operators, the operator mixing. This transformation allows us to introduce the parallel transport of the operators along the RG trajectory. The connection on this one-dimensional manifold governs the scale evolution of the operator mixing. It is shown that the solution of the eigenvalue problem of the connection gives the various scaling regimes and the relevant operators there. The relation to perturbative renormalization is also discussed in the framework of the $\phi^3$ theory in dimension $d=6$.

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