From Conformal Field Theory to Quantum Mechanics and Quantum Information

从共形场论到量子力学和量子信息

• 批准号: RGPIN-2015-05809
• 负责人: Walton, Mark
• 金额: $ 1.38万
• 依托单位: University of Lethbridge
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=613763
• 关键词: Conformal; Field; Theory; Quantum; Mechanics

I propose to perform research in two important topics in theoretical physics: conformal field theory (CFT) and quantum mechanics (QM). My objective in both areas is to improve theoretical understanding, thereby paving the way to physical applications, both known and new. CFT is a rich and deep subject, with many physical applications. CFTs describe systems at criticality, the world sheets of strings, quantum impurity problems, and are non-perturbatively solvable models for other physical quantum field theories. Much progress in understanding CFT, including many of my contributions, has come from the study of Wess-Zumino-Witten (WZW) models and related systems. Maintaining that approach, I aim to study the WZW models at fractional level, as prototypes of logarithmic CFTs; and investigate the phase model realizations of WZW fusion. QM is fundamental in physics. My approach is to study simple systems, from non-standard points of view, to extract new insights that apply more generally. Phase-space QM is one (relatively) uncommon point of view that I study, and intend to continue to examine. In addition, I aim to generalize my past work on the renormalization-group analysis of contact interactions, as well as investigate QM in a discretized alcove. In addition to continuing my research programs in CFT and QM, I plan to shift emphasis from CFT to QM, by initiating a new line of investigation in the theory of quantum information (QI). Due to its connection with quantum computation, and the light it has shone on the fundamentals of QM, QI is currently a very exciting theme. My background in CFT gives me a point of view that is rare in QI, and techniques that should prove useful. For example, the quantum marginal problem is crucial in QI, since its goal is to understand the possible states of a subsystem of a composite system. In this area many of the tools I have exploited in CFT have played important roles. In the short term, I am studying the QI uses of complex orthogonal designs, and in the longer term, I plan to investigate the relation between quantum marginality and the open dynamics of reduced systems. My proposal describes a strategic mix of reliable sources of fruitful research, and new, exciting work.   It creates the opportunity for significant training of highly-qualified personnel at all levels and facilitates collaboration in Alberta (there are strong groups in Edmonton and Calgary with interests in CFT and QI, respectively), Canada, and beyond.

我建议对理论物理中的两个重要课题进行研究：共形场理论(CFT)和量子力学(QM)。我在这两个领域的目标都是提高对理论的理解，从而为物理应用铺平道路，无论是已知的还是新的。 CFT是一门丰富而深入的学科，有着许多物理应用。CFTS描述了处于临界状态的系统、弦的世界薄片、量子杂质问题，并且是其他物理量子场理论的非微扰可解模型。 在理解CFT方面的许多进展，包括我的许多贡献，都来自于对Wess-Zumino-Witten(WZW)模型和相关系统的研究。保持这种方法，我的目标是在分数水平上研究WZW模型，作为对数CFT的原型；并研究WZW融合的阶段模型实现。 QM是物理学的基础。我的方法是从非标准的角度研究简单的系统，以提取更普遍适用的新见解。 相空间QM是我研究并打算继续研究的一个(相对)不常见的观点。此外，我的目标是推广我过去在接触相互作用的重整化-群分析方面的工作，以及在离散凹穴中研究QM。 除了继续我在CFT和QM方面的研究计划外，我还计划通过启动量子信息理论(QI)的新研究路线，将重点从CFT转移到QM。由于它与量子计算的联系，以及它对QM基础的启发，QI目前是一个非常令人兴奋的主题。 我在CFT的背景给了我一个在QI中很少见的观点，以及应该被证明有用的技术。例如，量子边际问题在QI中是至关重要的，因为它的目标是了解复合系统的一个子系统的可能状态。在这方面，我在CFT中开发的许多工具都发挥了重要作用。 短期内，我正在研究复正交设计的QI应用，长期而言，我计划研究量子边际性和约化系统的开放动力学之间的关系。 我的提案描述了一个战略组合，既有成果丰富的研究的可靠来源，又有新的、令人兴奋的工作。它为各级高素质人员的大量培训创造了机会，并促进了在艾伯塔省(埃德蒙顿和卡尔加里有强大的集团分别对CFT和QI感兴趣)、加拿大和其他地区的合作。