Dimensional renormalization in \(p\)-adic models of field theory
type: Item
instance of: scholarly article
title: Dimensional renormalization in \(p\)-adic models of field theory
zbMATH Open document ID: 1066.81590
DOI: 10.1007/BF02551034
author: R. Smith
published in: Theoretical and Mathematical Physics
publication date: 2000-01-01T00:00:00Z
review text: The authors define Feynman integrals with \(p\)-adic arguments of a complex dimension. Such an integral \(F_G(y,\lambda ,d)\) (determined by a graph \(G\)) depends on a \(p\)-adic vector \(y\), a collection \(\lambda\) of complex parameters, and the dimension \(d\). It is shown that \(F_G\) is meromorphic with respect to \(\lambda\) and \(d\) for a fixed \(y\). Then it is considered as a distribution in \(y\) which admits an analytic continuation with respect to \(d\); poles of the extended function are studied. Their location depends on the structure of \(G\). This makes it possible to carry out dimensional renormalization for the \(p\)-adic case. For the fermionic model another procedure of dimensional renormalization is given, based on renormalization group properties of a hierarchical model which provides a discretization for the \(p\)-adic quantum field model.
Mathematics Subject Classification ID: 81T17
Mathematics Subject Classification ID: 81Q30
Mathematics Subject Classification ID: 46S10
zbMATH DE Number: 1551636
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02551034
OpenAlex ID: W2059224262
description: scientific article; zbMATH DE number 1551636