Improving the understanding and the applicability of regularization by dimensional reduction for ultraviolet and infrared divergences

通过对紫外和红外发散进行降维来提高对正则化的理解和适用性

• 批准号: 192290006
• 负责人: Professor Dr. Dominik Stöckinger
• 金额: --
• 依托单位: Institut für Kern- und Teilchenphysik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2011
• 资助国家: 德国
• 起止时间: 2010-12-31 至 2014-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/192290006?language=en
• 关键词: Improving; understanding; applicability; regularization; dimensional

Regularization is a fundamental step in the renormalization of quantum field theories. It replaces divergent integrals by well-defined expressions and thus allows a mathematically consistent definition of quantum field theories. For practical purposes it is desirable that a regularization scheme preserves as many fundamental properties (such as Lorentz invariance or other symmetries) as possible, but no ideal scheme exists. We consider regularization by dimensional reduction (DRED). Particularly for supersymmetric theories DRED is often the best choice. However, several problems of DRED have been known for decades. In spite of recent progress, these problems have again been highlighted by the report of the SPA (“Supersymmetry Parameter Analysis”) collaboration, a world-wide collaboration with more than 100 authors. Our research project is precisely focused on the two most pressing problems of DRED: consistency with supersymmetry and consistency with factorization of infrared divergences. We will give definite answers by proving supersymmetry of DRED in several cases, identifying and describing cases where DRED violates supersymmetry, and by proving consistency with factorization at the two-loop level. Furthermore, we will provide easy-to-use transition rules between DRED and dimensional regularization (DREG). In this way we will significantly improve the theoretical understanding and the practical applicability of DRED and complete one of the seven tasks put forward by the SPA report.

正则化是量子场论重整化的基本步骤。它用定义明确的表达式取代发散积分，从而允许量子场论的数学一致性定义。出于实际目的，期望正则化方案尽可能地保留基本性质（例如洛伦兹不变性或其他对称性），但不存在理想的方案。我们考虑降维正则化（DRED）。特别是对于超对称理论，DRED通常是最好的选择。然而，几十年来，DRED的几个问题已经众所周知。尽管最近取得了一些进展，但SPA（“超对称参数分析”）合作组织的报告再次强调了这些问题，SPA是一个由100多位作者组成的全球合作组织。我们的研究项目正是集中在DRED的两个最紧迫的问题：与超对称性的一致性和与红外发散因子分解的一致性。我们将给出明确的答案，证明超对称性的DRED在几种情况下，确定和描述的情况下，DRED违反超对称性，并通过证明与因子分解在两个循环水平的一致性。此外，我们将提供DRED和维正则化（DREG）之间的易于使用的过渡规则。这样，我们将大大提高对DRED的理论理解和实际适用性，并完成SPA报告提出的七项任务之一。