Quantum effects of classical phase space singularities in lattice gauge models

晶格规范模型中经典相空间奇点的量子效应

• 批准号: 389090207
• 负责人: Dr. Matthias Schmidt
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 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 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/389090207?language=en
• 关键词: Quantum; effects; classical; phase; space

Gauge theories are the proper tool for describing the fundamental interactions between elementary particles. In the framework of renormalized perturbation theory, they reproduce the experimental data with extraordinary precision. There are however several phenomena which cannot be treated satisfactorily by means of perturbation theory, like the Gribov problem, certain anomalies, quark confinement or, more generally, the existence of bound states. To enter the discussion of such phenomena, one needs a deeper understanding of the mathematical structure of gauge theories. Important aspects of this structure become manifest in the gauge orbit space, that is, the space of the physical degrees of freedom of the theory. Since the gauge orbit space is the quotient of a group action, it may contain singularities. It is a long-standing problem to clarify the role of these singularities in quantum theory. In the present project, this problem shall be studied systematically for SU(2)-lattice gauge models by means of a method which was developed recently by the author and others.

规范理论是描述基本粒子之间基本相互作用的合适工具。在重正化微扰理论的框架下，他们以非凡的精度再现了实验数据。然而，有几种现象不能通过微扰理论得到令人满意的处理，例如格里波夫问题、某些异常、夸克禁闭或更普遍的束缚态的存在。要进入对此类现象的讨论，需要对规范理论的数学结构有更深入的了解。这种结构的重要方面在规范轨道空间中显现出来，即理论的物理自由度空间。由于规范轨道空间是群作用的商，因此它可能包含奇点。阐明这些奇点在量子理论中的作用是一个长期存在的问题。在本项目中，将采用作者等人最近开发的方法，针对SU(2)-格子规范模型系统地研究这个问题。

项目成果

On a Connection Used in Deformation Quantization

论变形量化中的连接

• DOI: 10.5506/aphyspolb.52.359
• 发表时间: 2021
• 期刊: arXiv: Mathematical Physics
• 作者: G. Rudolph;M. Schmidt
• 通讯作者: M. Schmidt

Deformation Quantization and Homological Reduction of a Lattice Gauge Model

格子规范模型的变形量化和同调约简

• DOI: 10.1007/s00220-020-03896-w
• 发表时间: 2021
• 期刊: Communications in Mathematical Physics
• 影响因子: 2.4
• 作者: M. J. Pflaum ;G. Rudolph;M. Schmidt
• 通讯作者: M. Schmidt

Quasicharacters, recoupling calculus, and Hamiltonian lattice quantum gauge theory

准字符、重新耦合微积分和哈密顿格子量子规范理论

• DOI: 10.1063/5.0021365
• 发表时间: 2021
• 期刊: Journal of Mathematical Physics
• 影响因子: 1.3
• 作者: P. D. Jarvis;G. Rudolph;M. Schmidt
• 通讯作者: M. Schmidt