RG Equations and High Energy Behaviour in Non-Renormalizable Theories

Abstract

We suggest a novel view on non-renormalizable interactions. It is based on the usual BPHZ R-operation which is equally applicable to any local QFT independently whether it is renormalizable or not. As a playground we take the phi^4_D theory in D dimensions for D=4,6,8,10 and consider the four-point scattering amplitude on shell. We derive the generalized RG equation and find the solution valid for any D that sums up the leading logarithms in all orders of PT in full analogy with the renormalizable case. It is found that the scattering amplitude in the phi^4_D theory possesses the Landau pole at high energy for any D. We discuss the application of the proposed procedure to other non-renormalizable theories.

9 pages, 2 figures, pdflatex

References in corpus (2)

• The Structure of UV Divergences in Maximally Supersymmetric Gauge Theories
• Kinematically Dependent Renormalization

Cited by in corpus (4)

• Leading all-loop quantum contribution to the effective potential in general scalar field theory
• Renormalization group equations and the recurrence pole relations in pure quantum gravity
• UV Divergences, RG Equations and High Energy Behaviour of the Amplitudes in the Wess-Zumino Model with Quartic Interaction
• Exact summation of leading logs around $T\bar{T}$ deformation of $O(N+1)$-symmetric 2D QFTs