Collaborative Research: Renormalization, Path Integrals, and Applications of Conformal Quantum Mechanics, Singular Potentials, and Quantum Field Theory

合作研究：重整化、路径积分以及共形量子力学、奇异势和量子场论的应用

• 批准号: 0308435
• 负责人: Carlos Ordonez
• 金额: $ 3.35万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0308435&HistoricalAwards=false
• 关键词: Collaborative; Research; Renormalization; Path; Integrals

The proposed research will focus on the theory and application of singular potentials and their relationship to quantum field theory. Particular emphasis will be given to those systems exhibiting asymptotic ultraviolet conformal invariance. The conformal anomaly will be analyzed in quantum mechanics problems that have applications in molecular physics such as the anisotropic inverse square potential. Path integral methods will be used to study this problem as well as a whole family of conformally invariant interactions. A second project will be to compare two methods of analyzing conformally invariant problems, one being a renormalization group analysis and the other being the method of self-adjoint extensions. The third project is to understand whether black hole thermodynamics can be understood in terms of the near-horizon conformal symmetry of a scalar field. The fourth project is to understand the role of singular potentials in dimensional reduction schemes where the low energy physics is confined to a brane but gravity propagates in one extra dimension.

拟议的研究将集中在奇异势的理论和应用及其与量子场论的关系。 特别强调的是，这些系统表现出渐近紫外共形不变性。 共形异常将在量子力学问题中进行分析，这些问题在分子物理学中有应用，例如各向异性平方反比势。路径积分方法将被用来研究这个问题，以及整个家庭的共形不变的相互作用。 第二个项目将是比较两种方法分析共形不变的问题，一个是重整化群分析，另一个是自伴扩展的方法。 第三个项目是了解黑洞热力学是否可以用标量场的近视界共形对称来理解。 第四个项目是了解奇异势在降维方案中的作用，其中低能物理被限制在膜上，但引力在一个额外的维度中传播。