Dyson–Schwinger equations in minimal subtraction

IF 1.5 Q2 PHYSICS, MATHEMATICAL Annales de l Institut Henri Poincare D Pub Date : 2021-09-28 DOI:10.4171/aihpd/169
Paul-Hermann Balduf
{"title":"Dyson–Schwinger equations in minimal subtraction","authors":"Paul-Hermann Balduf","doi":"10.4171/aihpd/169","DOIUrl":null,"url":null,"abstract":"We compare the solutions of one-scale Dyson-Schwinger equations in the Minimal subtraction (MS) scheme to the solutions in kinematic (MOM) renormalization schemes. We establish that the MS-solution can be interpreted as a MOM-solution, but with a shifted renormalization point, where the shift itself is a function of the coupling. We derive relations between this shift and various renormalization group functions and counter terms in perturbation theory. As concrete examples, we examine three different one-scale Dyson-Schwinger equations, one based on the D=4 multiedge graph, one for the D=6 multiedge graph and one mathematical toy model. For each of the integral kernels, we examine both the linear and nine different non-linear Dyson-Schwinger equations. For the linear cases, we empirically find exact functional forms of the shift between MOM and MS renormalization points. For the non-linear DSEs, the results for the shift suggest a factorially divergent power series. We determine the leading asymptotic growth parameters and find them in agreement with the ones of the anomalous dimension. Finally, we present a tentative exact non-perturbative solution to one of the non-linear DSEs of the toy model.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"273 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de l Institut Henri Poincare D","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/aihpd/169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 4

Abstract

We compare the solutions of one-scale Dyson-Schwinger equations in the Minimal subtraction (MS) scheme to the solutions in kinematic (MOM) renormalization schemes. We establish that the MS-solution can be interpreted as a MOM-solution, but with a shifted renormalization point, where the shift itself is a function of the coupling. We derive relations between this shift and various renormalization group functions and counter terms in perturbation theory. As concrete examples, we examine three different one-scale Dyson-Schwinger equations, one based on the D=4 multiedge graph, one for the D=6 multiedge graph and one mathematical toy model. For each of the integral kernels, we examine both the linear and nine different non-linear Dyson-Schwinger equations. For the linear cases, we empirically find exact functional forms of the shift between MOM and MS renormalization points. For the non-linear DSEs, the results for the shift suggest a factorially divergent power series. We determine the leading asymptotic growth parameters and find them in agreement with the ones of the anomalous dimension. Finally, we present a tentative exact non-perturbative solution to one of the non-linear DSEs of the toy model.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
极小减法中的Dyson-Schwinger方程
我们比较了一尺度Dyson-Schwinger方程在最小减法(MS)格式下的解与运动(MOM)重整化格式下的解。我们建立了ms -解可以被解释为mom -解,但是具有移位的重整化点,其中移位本身是耦合的函数。导出了这种位移与微扰理论中各种重整化群函数和逆项之间的关系。作为具体的例子,我们研究了三种不同的单尺度Dyson-Schwinger方程,一种是基于D=4多边图的,一种是基于D=6多边图的,一种是数学玩具模型。对于每个积分核,我们检查了线性和九个不同的非线性Dyson-Schwinger方程。对于线性情况,我们经验地找到了MOM和MS重整化点之间位移的精确函数形式。对于非线性dse,位移的结果表明幂级数是阶乘发散的。我们确定了主要的渐近增长参数,并发现它们与异常维的渐近增长参数一致。最后,我们给出了一个玩具模型的非线性dse的暂定精确非摄动解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
2.30
自引率
0.00%
发文量
16
期刊最新文献
A vertex model for supersymmetric LLT polynomials Duality of orthogonal and symplectic random tensor models Second order cumulants: Second order even elements and $R$-diagonal elements Fluctuations of dimer heights on contracting square-hexagon lattices Reflection of stochastic evolution equations in infinite dimensional domains
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1