Gauge dependence and Dyson Schwinger equations II

规范相关性和 Dyson Schwinger 方程 II

• 批准号: 379766926
• 负责人: Professor Dr. Dirk Kreimer
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/379766926?language=en
• 关键词: Gauge; dependence; Dyson; Schwinger; equations

We aim at an understanding of gauge invariance in off-shell Green functions.Modern algebraic algebraic methods allow to attack the problem via the study of co-ideals in Hopf algebras. Green functions appear as solutions to fixed point equations in the Hochschild cohomology of these algebras and define in this manner the Dyson Schwinger equations. We concentrate our study on 4- and higher n-point functions, with external ghost-, gauge- and matter fields, in covariant linear and non-linear gauges and varying renormalization schemes. Using Lagrange multipliers such questions can also be studied for field theories in higher even dimensions and in the context of the operator product expansions.We will investigate universal properties across dimensions of such theories as suggested by the 1/N expansion, answering questions on relations to conformal field theory, the bootstrap and the a-Theorem.

我们的目标是理解脱离壳层格林函数的规范不变性。现代代数方法允许通过研究Hopf代数中的余理想来解决这个问题。格林函数在这些代数的Hochschild上同调中表现为不动点方程的解，并以这种方式定义了Dyson Schwinger方程。在协变的线性和非线性规范和变化的重整化方案中，我们集中研究了具有外部鬼场、规范场和物质场的4点和更高的n点函数。利用拉格朗日乘子，我们也可以在算符乘积展开的背景下研究高偶维场理论的此类问题。我们将研究由1/N展开所提出的此类理论的跨维度的普适性质，回答与共形场论、自举和a-定理的关系的问题。

项目成果

Self-consistency of off-shell Slavnov-Taylor identities in QCD

QCD 中离壳 Slavnov-Taylor 恒等式的自洽

• DOI: 10.1103/physrevd.100.085001
• 发表时间: 2019
• 期刊: Physical Review D
• 影响因子: 5
• 作者: J. A. Gracey;H. Kißler;D. Kreimer
• 通讯作者: D. Kreimer

Off-shell diagrammatics for quantum gravity

量子引力的离壳图解

• DOI: 10.1016/j.physletb.2021.136219
• 发表时间: 2021
• 期刊: Physics Letters B
• 影响因子: 4.4
• 作者: H. Kißler

Critical properties of the valence-bond-solid transition in lattice quantum electrodynamics

• DOI: 10.1103/physrevd.101.094505
• 发表时间: 2020-03
• 期刊: Physical Review D
• 影响因子: 5
• 作者: N. Zerf;R. Boyack;P. Marquard;J. Gracey;J. Maciejko