RG equations and high energy behaviour in non-renormalizable theories

RG equations and high energy behaviour in non-renormalizable theories

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 of whether it is renormalizable or not. As a playground we take the ϕD4 theory in D dimensions for D=4,6,8,10 and consider the four-point s...

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Main Author: D.I. Kazakov
Format: Article
Language:English
Published: Elsevier 2019-10-01
Series:Physics Letters B
Online Access:http://www.sciencedirect.com/science/article/pii/S0370269319305052
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spelling doaj-3e1fc4c6d91644ce9b5175444e9219242020-11-25T00:57:17ZengElsevierPhysics Letters B0370-26932019-10-01797RG equations and high energy behaviour in non-renormalizable theoriesD.I. Kazakov0Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia; Moscow Institute of Physics and Technology, Dolgoprudny, Russia; Correspondence to: Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia.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 of whether it is renormalizable or not. As a playground we take the ϕD4 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 ϕD4 theory possesses the Landau pole at high energy for any D. We discuss the application of the proposed procedure to other non-renormalizable theories. Keywords: Renormalization, UV divergences, Non-renormalizable interactionshttp://www.sciencedirect.com/science/article/pii/S0370269319305052
collection DOAJ
language English
format Article
sources DOAJ
author D.I. Kazakov
spellingShingle D.I. Kazakov
RG equations and high energy behaviour in non-renormalizable theories
Physics Letters B
author_facet D.I. Kazakov
author_sort D.I. Kazakov
title RG equations and high energy behaviour in non-renormalizable theories
title_short RG equations and high energy behaviour in non-renormalizable theories
title_full RG equations and high energy behaviour in non-renormalizable theories
title_fullStr RG equations and high energy behaviour in non-renormalizable theories
title_full_unstemmed RG equations and high energy behaviour in non-renormalizable theories
title_sort rg equations and high energy behaviour in non-renormalizable theories
publisher Elsevier
series Physics Letters B
issn 0370-2693
publishDate 2019-10-01
description 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 of whether it is renormalizable or not. As a playground we take the ϕD4 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 ϕD4 theory possesses the Landau pole at high energy for any D. We discuss the application of the proposed procedure to other non-renormalizable theories. Keywords: Renormalization, UV divergences, Non-renormalizable interactions
url http://www.sciencedirect.com/science/article/pii/S0370269319305052
work_keys_str_mv AT dikazakov rgequationsandhighenergybehaviourinnonrenormalizabletheories
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